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Questions and Answers
What is the primary purpose of a ratio?
What is the primary purpose of a ratio?
What is the result of cross-multiplication in proportion?
What is the result of cross-multiplication in proportion?
If two ratios are equal, what can be said about the quantities involved?
If two ratios are equal, what can be said about the quantities involved?
What is the theorem that states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally?
What is the theorem that states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally?
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What is the first step in solving proportional problems?
What is the first step in solving proportional problems?
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What is the property of proportion that states w/x = z/y?
What is the property of proportion that states w/x = z/y?
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Ratios are typically written in which form?
Ratios are typically written in which form?
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What do ratios not provide?
What do ratios not provide?
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What is the formula to find the area of a triangle?
What is the formula to find the area of a triangle?
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A quadrilateral with all sides of equal length is known as a?
A quadrilateral with all sides of equal length is known as a?
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What is the formula to find the area of a parallelogram?
What is the formula to find the area of a parallelogram?
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Which theorem states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally?
Which theorem states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally?
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What is the formula to find the area of a trapezium?
What is the formula to find the area of a trapezium?
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Which type of polygon has diagonals that bisect each other?
Which type of polygon has diagonals that bisect each other?
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What is the formula to find the area of a kite?
What is the formula to find the area of a kite?
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Which theorem states that if two triangles are equiangular, then the corresponding sides are in proportion and the triangles are similar?
Which theorem states that if two triangles are equiangular, then the corresponding sides are in proportion and the triangles are similar?
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What is the conclusion of the proportionality of triangles with the same height?
What is the conclusion of the proportionality of triangles with the same height?
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Which polygon has four right angles and all sides of equal length?
Which polygon has four right angles and all sides of equal length?
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If ∆ABC and ∆DEF are similar triangles, what can be concluded about the ratios of their corresponding sides?
If ∆ABC and ∆DEF are similar triangles, what can be concluded about the ratios of their corresponding sides?
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In the proof of the theorem 'Triangles with Sides in Proportion are Similar', what is the purpose of drawing GH?
In the proof of the theorem 'Triangles with Sides in Proportion are Similar', what is the purpose of drawing GH?
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What is the Pythagorean Theorem used to find?
What is the Pythagorean Theorem used to find?
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If ∆ABC and ∆DEF are equiangular triangles, what can be concluded about their corresponding sides?
If ∆ABC and ∆DEF are equiangular triangles, what can be concluded about their corresponding sides?
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What is the condition for two triangles to be similar?
What is the condition for two triangles to be similar?
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In the proof of the theorem 'Triangles with Sides in Proportion are Similar', what is the purpose of the construction of AD?
In the proof of the theorem 'Triangles with Sides in Proportion are Similar', what is the purpose of the construction of AD?
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What is the formula for the area of a triangle?
What is the formula for the area of a triangle?
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If two triangles are similar, what can be concluded about their corresponding angles?
If two triangles are similar, what can be concluded about their corresponding angles?
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What is the statement of the Pythagorean Theorem?
What is the statement of the Pythagorean Theorem?
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If ∆ABC and ∆DEF are similar triangles, what can be concluded about their areas?
If ∆ABC and ∆DEF are similar triangles, what can be concluded about their areas?
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What is the area of a triangle with a base of 6 units and a height of 8 units?
What is the area of a triangle with a base of 6 units and a height of 8 units?
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If two triangles have equal bases and are between the same parallel lines, what can be concluded about their areas?
If two triangles have equal bases and are between the same parallel lines, what can be concluded about their areas?
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What is the statement of the Proportion Theorem?
What is the statement of the Proportion Theorem?
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What is the Mid-point Theorem?
What is the Mid-point Theorem?
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What are the conditions for similarity of two polygons?
What are the conditions for similarity of two polygons?
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What is true about equiangular triangles?
What is true about equiangular triangles?
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What is the formula for the area of a triangle?
What is the formula for the area of a triangle?
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What can be concluded about two triangles if they have proportional corresponding sides?
What can be concluded about two triangles if they have proportional corresponding sides?
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What is the converse of the Mid-point Theorem?
What is the converse of the Mid-point Theorem?
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If two triangles are similar, what can be said about their corresponding sides?
If two triangles are similar, what can be said about their corresponding sides?
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What is the condition for two triangles to be similar?
What is the condition for two triangles to be similar?
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What is the formula for the area of a triangle?
What is the formula for the area of a triangle?
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What is the converse of the Pythagorean Theorem stating?
What is the converse of the Pythagorean Theorem stating?
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What can be said about the areas of two triangles with equal bases between the same parallel lines?
What can be said about the areas of two triangles with equal bases between the same parallel lines?
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What is the condition for two polygons to be similar?
What is the condition for two polygons to be similar?
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What is the relation between the corresponding sides of two equiangular triangles?
What is the relation between the corresponding sides of two equiangular triangles?
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What is the main purpose of a ratio in Euclidean geometry?
What is the main purpose of a ratio in Euclidean geometry?
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If ( \frac{a}{b} = \frac{c}{d} ), what is the reciprocal proportion?
If ( \frac{a}{b} = \frac{c}{d} ), what is the reciprocal proportion?
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In a triangle, if a line is drawn parallel to one side, what is the relationship between the divided sides?
In a triangle, if a line is drawn parallel to one side, what is the relationship between the divided sides?
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What is the name of the theorem that states if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally?
What is the name of the theorem that states if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally?
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If ( \frac{a}{b} = \frac{c}{d} ) and ( \frac{a}{c} = \frac{b}{d} ), what can be concluded?
If ( \frac{a}{b} = \frac{c}{d} ) and ( \frac{a}{c} = \frac{b}{d} ), what can be concluded?
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What is the first step in solving proportional problems?
What is the first step in solving proportional problems?
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If two triangles have proportional corresponding sides, what can be concluded?
If two triangles have proportional corresponding sides, what can be concluded?
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What is the definition of proportion in geometry?
What is the definition of proportion in geometry?
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What is the area of a parallelogram with a base of 8 units and a height of 5 units?
What is the area of a parallelogram with a base of 8 units and a height of 5 units?
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In a triangle, if the base is 6 units and the height is 8 units, what is the length of the median bisecting the base?
In a triangle, if the base is 6 units and the height is 8 units, what is the length of the median bisecting the base?
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If two triangles have proportional corresponding sides, what can be concluded about the triangles?
If two triangles have proportional corresponding sides, what can be concluded about the triangles?
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What is the formula to find the area of a kite?
What is the formula to find the area of a kite?
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What is the formula to find the area of a trapezium?
What is the formula to find the area of a trapezium?
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What is the conclusion of the proportionality of triangles with the same height?
What is the conclusion of the proportionality of triangles with the same height?
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If two triangles have equal bases and are between the same parallel lines, what can be concluded about their areas?
If two triangles have equal bases and are between the same parallel lines, what can be concluded about their areas?
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What is the property of proportion that states that if DE is parallel to BC in triangle ABC, then AD/DB = AE/EC?
What is the property of proportion that states that if DE is parallel to BC in triangle ABC, then AD/DB = AE/EC?
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What is the condition for two triangles to be similar?
What is the condition for two triangles to be similar?
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What is the statement of the Pythagorean Theorem?
What is the statement of the Pythagorean Theorem?
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What is true about equiangular triangles?
What is true about equiangular triangles?
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If two triangles are similar, what can be concluded about their corresponding angles?
If two triangles are similar, what can be concluded about their corresponding angles?
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What is true about the areas of two triangles with equal heights and bases of different lengths?
What is true about the areas of two triangles with equal heights and bases of different lengths?
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What is the condition for two triangles to be similar?
What is the condition for two triangles to be similar?
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What can be concluded about two triangles if they have proportional corresponding sides?
What can be concluded about two triangles if they have proportional corresponding sides?
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What is the Mid-point Theorem?
What is the Mid-point Theorem?
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What is the Proportion Theorem?
What is the Proportion Theorem?
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If two polygons are similar, what can be concluded about their corresponding sides?
If two polygons are similar, what can be concluded about their corresponding sides?
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What is the converse of the Mid-point Theorem?
What is the converse of the Mid-point Theorem?
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What is the condition for two polygons to be similar?
What is the condition for two polygons to be similar?
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What is the consequence of the square of one side of a triangle being equal to the sum of the squares of the other two sides?
What is the consequence of the square of one side of a triangle being equal to the sum of the squares of the other two sides?
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What is the condition for two triangles to be similar?
What is the condition for two triangles to be similar?
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If two triangles are equiangular, what can be said about their corresponding sides?
If two triangles are equiangular, what can be said about their corresponding sides?
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What is the formula for the area of a triangle?
What is the formula for the area of a triangle?
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If two triangles have equal bases and are between the same parallel lines, what can be concluded about their areas?
If two triangles have equal bases and are between the same parallel lines, what can be concluded about their areas?
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What is the result of the similarity of ΔCAD and ΔCBA?
What is the result of the similarity of ΔCAD and ΔCBA?
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If ∆ABC and ∆DEF are similar triangles, what can be concluded about their corresponding angles?
If ∆ABC and ∆DEF are similar triangles, what can be concluded about their corresponding angles?
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What is the consequence of having triangles with corresponding sides in proportion?
What is the consequence of having triangles with corresponding sides in proportion?
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What is the purpose of drawing GH in the proof of the theorem 'Triangles with Sides in Proportion are Similar'?
What is the purpose of drawing GH in the proof of the theorem 'Triangles with Sides in Proportion are Similar'?
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What can be concluded about the areas of two triangles with equal heights and bases of ratio 2:3?
What can be concluded about the areas of two triangles with equal heights and bases of ratio 2:3?
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In the Pythagorean Theorem, what is the relation between the square on the hypotenuse and the sum of the squares on the other two sides?
In the Pythagorean Theorem, what is the relation between the square on the hypotenuse and the sum of the squares on the other two sides?
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What is the condition for two triangles to be similar?
What is the condition for two triangles to be similar?
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If ∆ABC and ∆DEF are similar triangles, what can be concluded about their areas?
If ∆ABC and ∆DEF are similar triangles, what can be concluded about their areas?
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What is the statement of the theorem 'Triangles with Sides in Proportion are Similar'?
What is the statement of the theorem 'Triangles with Sides in Proportion are Similar'?
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What is true about the areas of two triangles with equal bases between the same parallel lines?
What is true about the areas of two triangles with equal bases between the same parallel lines?
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What is the formula for the area of a triangle?
What is the formula for the area of a triangle?
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If $\frac{a}{b} = \frac{c}{d}$ and $a = 2c$, what is the value of $\frac{b}{d}$?
If $\frac{a}{b} = \frac{c}{d}$ and $a = 2c$, what is the value of $\frac{b}{d}$?
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In triangle $\triangle ABC$, if $\overline{DE}$ is parallel to $\overline{BC}$, what is the value of $\frac{AD}{DB}$ if $AE = 4EC$?
In triangle $\triangle ABC$, if $\overline{DE}$ is parallel to $\overline{BC}$, what is the value of $\frac{AD}{DB}$ if $AE = 4EC$?
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If $\frac{w}{x} = \frac{y}{z}$, what is the value of $\frac{x}{w}$?
If $\frac{w}{x} = \frac{y}{z}$, what is the value of $\frac{x}{w}$?
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In triangle $\triangle ABC$, if $\overline{DE}$ is parallel to $\overline{BC}$, what is the relationship between $AD$, $DB$, $AE$, and $EC$?
In triangle $\triangle ABC$, if $\overline{DE}$ is parallel to $\overline{BC}$, what is the relationship between $AD$, $DB$, $AE$, and $EC$?
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If $\frac{a}{b} = \frac{c}{d}$, what is the value of $\frac{a+c}{b+d}$?
If $\frac{a}{b} = \frac{c}{d}$, what is the value of $\frac{a+c}{b+d}$?
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If $\frac{w}{x} = \frac{y}{z}$, what is the value of $\frac{w-y}{x-z}$?
If $\frac{w}{x} = \frac{y}{z}$, what is the value of $\frac{w-y}{x-z}$?
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In triangle $\triangle ABC$, if $\overline{DE}$ is parallel to $\overline{BC}$, what is the value of $\frac{AE}{EC}$ if $AD = 2DB$?
In triangle $\triangle ABC$, if $\overline{DE}$ is parallel to $\overline{BC}$, what is the value of $\frac{AE}{EC}$ if $AD = 2DB$?
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If $\frac{a}{b} = \frac{c}{d}$, what is the value of $\frac{a+b}{c+d}$?
If $\frac{a}{b} = \frac{c}{d}$, what is the value of $\frac{a+b}{c+d}$?
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If two triangles have proportional corresponding sides, what can be concluded about their corresponding angles?
If two triangles have proportional corresponding sides, what can be concluded about their corresponding angles?
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What is the condition for two polygons to be similar?
What is the condition for two polygons to be similar?
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What is the formula to find the area of a kite?
What is the formula to find the area of a kite?
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If two triangles are similar, what can be concluded about their areas?
If two triangles are similar, what can be concluded about their areas?
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What is the relation between the corresponding sides of two equiangular triangles?
What is the relation between the corresponding sides of two equiangular triangles?
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What is the converse of the Pythagorean Theorem stating?
What is the converse of the Pythagorean Theorem stating?
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What is the formula to find the area of a trapezium?
What is the formula to find the area of a trapezium?
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If two triangles are similar, what can be concluded about their corresponding sides?
If two triangles are similar, what can be concluded about their corresponding sides?
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What is the condition for two triangles to be similar?
What is the condition for two triangles to be similar?
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What is the name of the theorem that states if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally?
What is the name of the theorem that states if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally?
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If two triangles have proportional corresponding sides, what can be concluded about their corresponding angles?
If two triangles have proportional corresponding sides, what can be concluded about their corresponding angles?
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What can be concluded about two triangles if they have proportional corresponding sides?
What can be concluded about two triangles if they have proportional corresponding sides?
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What is the condition for similarity of two polygons?
What is the condition for similarity of two polygons?
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What is the statement of the Proportion Theorem?
What is the statement of the Proportion Theorem?
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What is the conclusion of the Mid-point Theorem?
What is the conclusion of the Mid-point Theorem?
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What is the condition for similarity of two polygons?
What is the condition for similarity of two polygons?
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If two triangles are equiangular, what can be concluded about their corresponding sides?
If two triangles are equiangular, what can be concluded about their corresponding sides?
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What is the converse of the Mid-point Theorem?
What is the converse of the Mid-point Theorem?
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What is the formula for the area of a triangle with a base of 10 units and a height of 12 units?
What is the formula for the area of a triangle with a base of 10 units and a height of 12 units?
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If two triangles have proportional corresponding sides, what can be concluded about their areas?
If two triangles have proportional corresponding sides, what can be concluded about their areas?
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If ∆ABC and ∆DEF are similar triangles, and AB = 6, BC = 8, and DE = 3, what is the length of EF?
If ∆ABC and ∆DEF are similar triangles, and AB = 6, BC = 8, and DE = 3, what is the length of EF?
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If ∆ABC and ∆DEF are equiangular triangles, and AB = 4, BC = 5, and DE = 2, what is the length of EF?
If ∆ABC and ∆DEF are equiangular triangles, and AB = 4, BC = 5, and DE = 2, what is the length of EF?
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In the proof of the theorem 'Triangles with Sides in Proportion are Similar', what is the purpose of drawing GH?
In the proof of the theorem 'Triangles with Sides in Proportion are Similar', what is the purpose of drawing GH?
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What is the condition for two triangles to be similar?
What is the condition for two triangles to be similar?
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What is the Pythagorean Theorem used to find?
What is the Pythagorean Theorem used to find?
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If two triangles have equal bases and are between the same parallel lines, what can be concluded about their areas?
If two triangles have equal bases and are between the same parallel lines, what can be concluded about their areas?
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What can be concluded about two triangles if they have proportional corresponding sides?
What can be concluded about two triangles if they have proportional corresponding sides?
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What is the relation between the corresponding sides of two equiangular triangles?
What is the relation between the corresponding sides of two equiangular triangles?
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What is the formula to find the area of a triangle with a base of 6 units and a height of 8 units?
What is the formula to find the area of a triangle with a base of 6 units and a height of 8 units?
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If ∆ABC and ∆DEF are similar triangles, what can be concluded about their corresponding angles?
If ∆ABC and ∆DEF are similar triangles, what can be concluded about their corresponding angles?
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What is the necessary and sufficient condition for a triangle to have a right angle?
What is the necessary and sufficient condition for a triangle to have a right angle?
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If ∆ABC and ∆DEF are similar triangles, what can be said about their corresponding sides?
If ∆ABC and ∆DEF are similar triangles, what can be said about their corresponding sides?
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What is the area of a triangle with a base of 5 units and a height of 12 units?
What is the area of a triangle with a base of 5 units and a height of 12 units?
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If two triangles are equiangular, what can be said about their corresponding sides?
If two triangles are equiangular, what can be said about their corresponding sides?
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What is the condition for two polygons to be similar?
What is the condition for two polygons to be similar?
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What is the converse of the Pythagorean Theorem stating?
What is the converse of the Pythagorean Theorem stating?
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