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Questions and Answers
What is the condition for two triangles to be similar according to the similarity conditions?
What is the condition for two triangles to be similar according to the similarity conditions?
- At least two pairs of corresponding angles are equal
- All pairs of corresponding sides are in the same proportion, but corresponding angles may differ
- At least one pair of corresponding angles are equal, and at least one pair of corresponding sides are in the same proportion
- All pairs of corresponding angles are equal, and all pairs of corresponding sides are in the same proportion (correct)
What can be concluded if two triangles have equal heights?
What can be concluded if two triangles have equal heights?
- Their areas are proportional to their bases (correct)
- They are similar triangles
- They have equal bases
- They have equal areas
What is the definition of similar polygons?
What is the definition of similar polygons?
- Polygons that have the same shape but differ in size. (correct)
- Polygons that have the same size but differ in shape.
- Polygons that are congruent and have the same shape and size.
- Polygons that are congruent and have different shapes and sizes.
What is the formula for the area of a triangle?
What is the formula for the area of a triangle?
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?
What are the two conditions for two polygons to be similar?
What are the two conditions for two polygons to be similar?
What is the minimum number of conditions required to prove two triangles are similar?
What is the minimum number of conditions required to prove two triangles are similar?
What is the condition for two triangles to be equiangular?
What is the condition for two triangles to be equiangular?
What is the theorem that states equiangular triangles are similar?
What is the theorem that states equiangular triangles are similar?
What can be concluded if GH is parallel to BC in ∆ABC?
What can be concluded if GH is parallel to BC in ∆ABC?
What is the theorem that states triangles with sides in proportion are similar?
What is the theorem that states triangles with sides in proportion are similar?
What is the first step in the proof of the theorem that equiangular triangles are similar?
What is the first step in the proof of the theorem that equiangular triangles are similar?
What can be said about the areas of ∆ABC and ∆DEF if they are similar triangles?
What can be said about the areas of ∆ABC and ∆DEF if they are similar triangles?
What is the required result to prove that two triangles are similar?
What is the required result to prove that two triangles are similar?
What is true about congruent polygons?
What is true about congruent polygons?
What is the minimum number of sides required for two polygons to be similar?
What is the minimum number of sides required for two polygons to be similar?
Which of the following is a necessary condition for two polygons to be similar?
Which of the following is a necessary condition for two polygons to be similar?
If ∆ABC is similar to ∆PQR, what can be said about ∠A and ∠P?
If ∆ABC is similar to ∆PQR, what can be said about ∠A and ∠P?
What can be concluded if ∆ABC and ∆DEF have corresponding sides in the same proportion?
What can be concluded if ∆ABC and ∆DEF have corresponding sides in the same proportion?
Which of the following is an alternative way to prove that two triangles are similar?
Which of the following is an alternative way to prove that two triangles are similar?
What is the name of the theorem that states equiangular triangles are similar?
What is the name of the theorem that states equiangular triangles are similar?
What is the advantage of using the equiangular triangles condition to prove similarity?
What is the advantage of using the equiangular triangles condition to prove similarity?
If two polygons are similar, what can be said about their corresponding sides?
If two polygons are similar, what can be said about their corresponding sides?
What is the minimum number of sides required for two polygons to be similar?
What is the minimum number of sides required for two polygons to be similar?
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?
If ∆ABC and ∆DEF are similar, what is the relationship between their corresponding angles?
If ∆ABC and ∆DEF are similar, what is the relationship between their corresponding angles?
What is the purpose of constructing GH in the proof of the theorem that triangles with proportional sides are similar?
What is the purpose of constructing GH in the proof of the theorem that triangles with proportional sides are similar?
What is the converse of the theorem that equiangular triangles are similar?
What is the converse of the theorem that equiangular triangles are similar?
If ∆ABC and ∆DEF are similar, what can be said about their corresponding heights?
If ∆ABC and ∆DEF are similar, what can be said about their corresponding heights?
What is the condition for two triangles to be equiangular?
What is the condition for two triangles to be equiangular?
If two triangles have equal corresponding heights, what can be concluded about their areas?
If two triangles have equal corresponding heights, what can be concluded about their areas?
What is the purpose of the proportionality theorem in the proof of the theorem that triangles with proportional sides are similar?
What is the purpose of the proportionality theorem in the proof of the theorem that triangles with proportional sides are similar?
If two polygons are similar, which of the following statements is true?
If two polygons are similar, which of the following statements is true?
What is the primary difference between congruent and similar polygons?
What is the primary difference between congruent and similar polygons?
If ∆ABC is similar to ∆PQR, what can be said about the corresponding sides?
If ∆ABC is similar to ∆PQR, what can be said about the corresponding sides?
What is the minimum number of conditions required to prove two triangles are similar?
What is the minimum number of conditions required to prove two triangles are similar?
Which of the following is NOT a necessary condition for two polygons to be similar?
Which of the following is NOT a necessary condition for two polygons to be similar?
What can be concluded about ∆ABC and ∆DEF if they have corresponding sides in the same proportion?
What can be concluded about ∆ABC and ∆DEF if they have corresponding sides in the same proportion?
What is the purpose of the theorem that equiangular triangles are similar?
What is the purpose of the theorem that equiangular triangles are similar?
If two triangles are similar, what can be said about their corresponding angles?
If two triangles are similar, what can be said about their corresponding angles?
In the proof of the theorem that triangles with sides in proportion are similar, what is the purpose of constructing GH such that AG = DE and AH = DF?
In the proof of the theorem that triangles with sides in proportion are similar, what is the purpose of constructing GH such that AG = DE and AH = DF?
What is the key concept used in the proof that triangles with sides in proportion are similar?
What is the key concept used in the proof that triangles with sides in proportion are similar?
What is the conclusion that can be drawn if two triangles have corresponding sides in the same proportion?
What is the conclusion that can be drawn if two triangles have corresponding sides in the same proportion?
What is the necessary condition for two triangles to be similar?
What is the necessary condition for two triangles to be similar?
What is the relationship between the areas of two similar triangles?
What is the relationship between the areas of two similar triangles?
What is the purpose of the proportionality theorem in the proof of the theorem that triangles with proportional sides are similar?
What is the purpose of the proportionality theorem in the proof of the theorem that triangles with proportional sides are similar?
What is the key concept used in the proof that equiangular triangles are similar?
What is the key concept used in the proof that equiangular triangles are similar?
What is the conclusion that can be drawn if two triangles are similar?
What is the conclusion that can be drawn if two triangles are similar?
If two polygons have the same number of sides and are similar, what can be concluded about their corresponding angles?
If two polygons have the same number of sides and are similar, what can be concluded about their corresponding angles?
What is the minimum requirement for two polygons to be similar?
What is the minimum requirement for two polygons to be similar?
If ∆ABC and ∆DEF are similar, what can be said about their corresponding medians?
If ∆ABC and ∆DEF are similar, what can be said about their corresponding medians?
What is the advantage of using the condition of equal corresponding angles to prove similarity?
What is the advantage of using the condition of equal corresponding angles to prove similarity?
If two triangles have proportional corresponding sides, what can be concluded about their corresponding altitudes?
If two triangles have proportional corresponding sides, what can be concluded about their corresponding altitudes?
What is the primary difference between congruent and similar polygons?
What is the primary difference between congruent and similar polygons?
If ∆ABC and ∆DEF are equiangular, what can be concluded about their corresponding sides?
If ∆ABC and ∆DEF are equiangular, what can be concluded about their corresponding sides?
What is the purpose of the theorem that equiangular triangles are similar?
What is the purpose of the theorem that equiangular triangles are similar?
What is the main purpose of proving ∆AGH ∼ ∆ABC in the theorem that triangles with sides in proportion are similar?
What is the main purpose of proving ∆AGH ∼ ∆ABC in the theorem that triangles with sides in proportion are similar?
What is the condition required to prove that two polygons are similar?
What is the condition required to prove that two polygons are similar?
What is the advantage of using the theorem that triangles with sides in proportion are similar?
What is the advantage of using the theorem that triangles with sides in proportion are similar?
What is the relationship between the areas of ∆ABC and ∆DEF if ∆ABC ∼ ∆DEF?
What is the relationship between the areas of ∆ABC and ∆DEF if ∆ABC ∼ ∆DEF?
What is the purpose of constructing Q on CA such that CQ = FD in the theorem that triangles with sides in proportion are similar?
What is the purpose of constructing Q on CA such that CQ = FD in the theorem that triangles with sides in proportion are similar?
What can be concluded about ∆ABC and ∆DEF if ∆ABC ∼ ∆DEF and AB / DE = AC / DF?
What can be concluded about ∆ABC and ∆DEF if ∆ABC ∼ ∆DEF and AB / DE = AC / DF?
What is the condition required to prove that two triangles are equiangular?
What is the condition required to prove that two triangles are equiangular?
What is the main idea behind the proportionality theorem?
What is the main idea behind the proportionality theorem?
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