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Questions and Answers
Which segments are skew to segment BC?
Which segments are skew to segment BC?
Which theorem or postulate can be used to prove the similarity of the two given triangles?
Which theorem or postulate can be used to prove the similarity of the two given triangles?
A tree casts a shadow 14 feet long. The angle from the tip of the shadow to the top of the tree is 60 degrees. What is the approximate height of the tree?
A tree casts a shadow 14 feet long. The angle from the tip of the shadow to the top of the tree is 60 degrees. What is the approximate height of the tree?
Given a║b, m∠3 = $5x+10$, and m∠5 = $3x+10$, find the value of x.
Given a║b, m∠3 = $5x+10$, and m∠5 = $3x+10$, find the value of x.
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In circle C, arc AB = 72 degrees and AD is a diameter. What is the measure of angle BCD?
In circle C, arc AB = 72 degrees and AD is a diameter. What is the measure of angle BCD?
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If m∠3 = $5x$ and m∠6 = $3x + 20$, and lines a and b are parallel, determine the value of x.
If m∠3 = $5x$ and m∠6 = $3x + 20$, and lines a and b are parallel, determine the value of x.
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Given the diagram, what is the correct expression to represent the length of segment CD?
Given the diagram, what is the correct expression to represent the length of segment CD?
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Given a set of parallel lines, which relationship is false?
Given a set of parallel lines, which relationship is false?
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Given two angles measuring 90°, which statement represents the inverse regarding them being complementary?
Given two angles measuring 90°, which statement represents the inverse regarding them being complementary?
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Which of the following is the best example of deductive reasoning?
Which of the following is the best example of deductive reasoning?
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Given that AF is congruent to DE, AB is congruent to FC, and AB is parallel to FC, which theorem or postulate proves triangle ABE is congruent to triangle FCD?
Given that AF is congruent to DE, AB is congruent to FC, and AB is parallel to FC, which theorem or postulate proves triangle ABE is congruent to triangle FCD?
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Which of the following is a necessary property of all parallelograms?
Which of the following is a necessary property of all parallelograms?
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In the given figure, if angle TSR (the whole angle) measures 4x degrees and angle T is equal to 32 degrees, then what is the value of angle S?
In the given figure, if angle TSR (the whole angle) measures 4x degrees and angle T is equal to 32 degrees, then what is the value of angle S?
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In the provided diagram, which trigonometric function can be used to determine the angle of depression from the pier to the toy sailboat?
In the provided diagram, which trigonometric function can be used to determine the angle of depression from the pier to the toy sailboat?
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What is the error in Joanna's reasoning regarding the diagonals of a figure?
What is the error in Joanna's reasoning regarding the diagonals of a figure?
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What are the coordinates of the midpoint of the line segment JK, where J(-1, 2) and K(6, 8)?
What are the coordinates of the midpoint of the line segment JK, where J(-1, 2) and K(6, 8)?
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Based on the diagram, which theorem or postulate can be used to prove triangle JKL is congruent to triangle MNL ?
Based on the diagram, which theorem or postulate can be used to prove triangle JKL is congruent to triangle MNL ?
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Given three vertices of a square (3, 1), (4, -4) and (-1, -5), what are the coordinates of the intersection point, Q, of the diagonals?
Given three vertices of a square (3, 1), (4, -4) and (-1, -5), what are the coordinates of the intersection point, Q, of the diagonals?
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Tiana makes the conjecture that prime numbers must be odd based on the examples 3, 5, 7, 11. Which statement is true regarding Tiana's conjecture?
Tiana makes the conjecture that prime numbers must be odd based on the examples 3, 5, 7, 11. Which statement is true regarding Tiana's conjecture?
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In the context of the pier and sailboat problem, if the height of the pier is 6 feet and the horizontal distance to the sailboat is 4 feet, what is the approximate angle of depression?
In the context of the pier and sailboat problem, if the height of the pier is 6 feet and the horizontal distance to the sailboat is 4 feet, what is the approximate angle of depression?
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If triangle JKL is congruent to triangle MNL, which side in triangle MNL corresponds to side JL in triangle JKL?
If triangle JKL is congruent to triangle MNL, which side in triangle MNL corresponds to side JL in triangle JKL?
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A property of all rectangles is:
A property of all rectangles is:
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What is the length of segment BI in a rectangular prism with dimensions 12 inches long, 5 inches wide, and 7 inches tall, where B and I are opposite corners of the prism?
What is the length of segment BI in a rectangular prism with dimensions 12 inches long, 5 inches wide, and 7 inches tall, where B and I are opposite corners of the prism?
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Point B is located at (-4, -6). Which reflection would result in B'(6, 4)?
Point B is located at (-4, -6). Which reflection would result in B'(6, 4)?
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In a 30-60-90 triangle HJK, where angle J is 30 degrees, angle K is 60 degrees, and side HJ is 5, what is the exact length of side HK which is opposite to the 60 degree angle?
In a 30-60-90 triangle HJK, where angle J is 30 degrees, angle K is 60 degrees, and side HJ is 5, what is the exact length of side HK which is opposite to the 60 degree angle?
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If you are traveling at 50 miles per hour, approximately how many feet per second are you moving?
If you are traveling at 50 miles per hour, approximately how many feet per second are you moving?
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Two similar triangles have corresponding sides with a ratio of 5:3. If the smaller triangle has an area of 108 sq. in., what is the area of the larger triangle?
Two similar triangles have corresponding sides with a ratio of 5:3. If the smaller triangle has an area of 108 sq. in., what is the area of the larger triangle?
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What additional information is required to calculate the length of the roof using the law of cosines given a diagram that shows the roof angle and the length of each side?
What additional information is required to calculate the length of the roof using the law of cosines given a diagram that shows the roof angle and the length of each side?
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If a triangular prism has 6 vertices, and 5 faces, how many edges does it have?
If a triangular prism has 6 vertices, and 5 faces, how many edges does it have?
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A house has a width $w$. Given the side lengths of 15 ft and 15 ft, what is the value of $w$?
A house has a width $w$. Given the side lengths of 15 ft and 15 ft, what is the value of $w$?
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Given the statement: 'The segment bisector is the midpoint,' what is the inverse of this statement?
Given the statement: 'The segment bisector is the midpoint,' what is the inverse of this statement?
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Triangle RST has vertices R(3, 3), S(6, -2), and T(0, -2). How can ΔRST be classified based on its sides?
Triangle RST has vertices R(3, 3), S(6, -2), and T(0, -2). How can ΔRST be classified based on its sides?
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Quadrilateral ABCD has $\overline{AB} ; ,, ,, ,, \overline{CD}$ and $\overline{AD} , ,, ,, \overline{BC}$ . What is the most specific name for quadrilateral ABCD?
Quadrilateral ABCD has $\overline{AB} ; ,, ,, ,, \overline{CD}$ and $\overline{AD} , ,, ,, \overline{BC}$ . What is the most specific name for quadrilateral ABCD?
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A calculator box has a volume of 29 cubic inches. Given that 1 inch = 2.54 centimeters, what is the volume of the calculator box to the nearest cubic centimeter?
A calculator box has a volume of 29 cubic inches. Given that 1 inch = 2.54 centimeters, what is the volume of the calculator box to the nearest cubic centimeter?
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What is the image of point Y(-4, 7) under the translation (x, y) → (x + 3, y - 5)?
What is the image of point Y(-4, 7) under the translation (x, y) → (x + 3, y - 5)?
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Given triangle △EFG with side lengths of 8 and 10, and triangle △DGH with side length 12, and that ∠E ≅ ∠D, what additional information is needed to prove the triangles are similar using Side-Angle-Side Similarity Theorem?
Given triangle △EFG with side lengths of 8 and 10, and triangle △DGH with side length 12, and that ∠E ≅ ∠D, what additional information is needed to prove the triangles are similar using Side-Angle-Side Similarity Theorem?
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In triangle ABC, with side lengths AB = 14.7, BC = 8.3, and AC = 16.9, what is the value of sin(C) rounded to the nearest hundredth?
In triangle ABC, with side lengths AB = 14.7, BC = 8.3, and AC = 16.9, what is the value of sin(C) rounded to the nearest hundredth?
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What is the midpoint of the line segment with endpoints (2, -5) and (-6, 4)?
What is the midpoint of the line segment with endpoints (2, -5) and (-6, 4)?
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A square has a diagonal of 7 cm. What is the length of one side of this square?
A square has a diagonal of 7 cm. What is the length of one side of this square?
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Which statement regarding geometric terms is correct?
Which statement regarding geometric terms is correct?
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What geometric term describes the intersection of two unique planes?
What geometric term describes the intersection of two unique planes?
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A quadrilateral is a parallelogram. If its two angles are defined by a and b, where one angle is a and its adjacent angle is $7b-32$, if the other angle is $10a+14$, which values of a and b make it into a parallelogram?
A quadrilateral is a parallelogram. If its two angles are defined by a and b, where one angle is a and its adjacent angle is $7b-32$, if the other angle is $10a+14$, which values of a and b make it into a parallelogram?
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In a right triangle with sides of length 5 and 13, determine the length of the hypotenuse of the right triangle with sides 5 and 13.
In a right triangle with sides of length 5 and 13, determine the length of the hypotenuse of the right triangle with sides 5 and 13.
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Lines l, m, and n are in the same plane. Line m is perpendicular to line l, and line n is also perpendicular to line l. What is the relationship between lines m and n?
Lines l, m, and n are in the same plane. Line m is perpendicular to line l, and line n is also perpendicular to line l. What is the relationship between lines m and n?
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What is the number of miles a person will run during a 5-kilometer race, given that 1 km ≈ 0.62 mi?
What is the number of miles a person will run during a 5-kilometer race, given that 1 km ≈ 0.62 mi?
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Study Notes
Geometry Practice Test - Study Notes
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Equilateral Triangles: In an equilateral triangle, all sides and angles are equal. If a triangle is equilateral, and one side is represented by an expression, set it equal to any other side to solve for the variable.
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Conditional Statements and Converse: A conditional statement has a hypothesis and a conclusion. The converse reverses the hypothesis and conclusion. If the converse is false, a counterexample illustrates this.
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Parallel Lines and Angles: If two parallel lines are cut by a transversal, the angles formed have certain relationships (e.g., alternate interior angles are congruent).
- Identify the relevant angles; use the parallel lines and corresponding angles to identify what is given and what you can deduce about other angles, then use that information to solve equations.
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Midpoints: A midpoint divides a line segment into two equal parts. The coordinates of the midpoint can be calculated with a formula, or geometrically on a diagram.
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Geometry Proof steps: A proof contains two sections, statements and reasons.
- Identify the given statements and the statements to prove.
- Use the given information or established rules of geometry to produce further statements.
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Angle of Depression: The angle of depression from one point to another is the angle formed by the horizontal line from the first point, and the line of sight from the first point to the second point, measured below the horizontal line. This can be solved using trigonometry.
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Properties of a Square: The diagonals of a square bisect each other, and the diagonals are perpendicular.
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Midsegment of a Triangle: The midsegment of a triangle is parallel to the third side and is half as long.
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Theorems of Congruence such as SSS, SAS, ASA, AAS
- These can be used to to determine if triangles are congruent, based upon the information given in the problem.
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Congruent Triangles and Corresponding Parts: Corresponding parts of congruent triangles are congruent. Prove triangles can be congruent based upon given information; use theorem or postulate.
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Coordinates of Points in Geometry: Given coordinates of points in a plane, calculate the midpoint or the length of a segment.
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Prime and Composite Numbers: Prime numbers have only two factors, 1 and themselves. Composite numbers have more than two factors. Be wary of conjecture questions (patterns in numbers); consider what the conjecture is based on, and what it is trying to prove.
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Inductive Reasoning vs. Deductive Reasoning: Inductive reasoning uses observations to draw a conclusion. Deductive reasoning starts with a general statement and applies it to specific cases.
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Trigonometry in Right Triangles: Use sine, cosine, or tangent ratios to find missing side lengths or angles in right triangles.
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Parallelogram determine if given properties prove shape is a parallelogram.
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Classifying quadrilaterals such as a square, rectangle, rhombus, and trapezoid based on the given properties.
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Volumes and Areas: Use formulas for areas and volumes.
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Equation of Lines: Find the equation for a line given a point on the line and the slope of the line.
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Ratio of Similarity with Volume: Relationship between the ratio of similar figures.
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Coordinate Geometry: Determine coordinates of points in a coordinate plane.
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Geometric Properties and Theorems: Use theorems to prove statements or solve for unknowns.
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Description
Test your understanding of key geometry concepts with this practice quiz. Topics include equilateral triangles, conditional statements, parallel lines, and finding midpoints. Perfect for reinforcing your knowledge and preparing for exams.
