Gr12 Mathematics: Ch 7.4 Similarity

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?

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?

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?

Area = 1/2 × base × height Signup and view all the answers

If ∆ABC and ∆DEF are similar triangles, what can be said about their corresponding sides?

They are in the same proportion Signup and view all the answers

What are the two conditions for two polygons to be similar?

All pairs of corresponding angles are equal and all pairs of corresponding sides are in the same proportion. Signup and view all the answers

What is the minimum number of conditions required to prove two triangles are similar?

One condition Signup and view all the answers

What is the condition for two triangles to be equiangular?

They have equal corresponding angles Signup and view all the answers

What is the theorem that states equiangular triangles are similar?

Theorem of Equiangular Triangles Signup and view all the answers

What can be concluded if GH is parallel to BC in ∆ABC?

∠AGH = ∠B Signup and view all the answers

What is the theorem that states triangles with sides in proportion are similar?

Theorem of Triangles with Sides in Proportion Signup and view all the answers

What is the first step in the proof of the theorem that equiangular triangles are similar?

Mark G on AB such that AG = DE, and mark H on AC such that AH = DF. Signup and view all the answers

What can be said about the areas of ∆ABC and ∆DEF if they are similar triangles?

They are proportional to their bases Signup and view all the answers

What is the required result to prove that two triangles are similar?

$\frac{AB}{DE} = \frac{AC}{DF} = \frac{BC}{EF}$ Signup and view all the answers

What is true about congruent polygons?

They are similar and have the same shape and size. Signup and view all the answers

What is the minimum number of sides required for two polygons to be similar?

The same number of sides Signup and view all the answers

Which of the following is a necessary condition for two polygons to be similar?

Both conditions must be true for all polygons Signup and view all the answers

If ∆ABC is similar to ∆PQR, what can be said about ∠A and ∠P?

They are equal Signup and view all the answers

What can be concluded if ∆ABC and ∆DEF have corresponding sides in the same proportion?

They are similar Signup and view all the answers

Which of the following is an alternative way to prove that two triangles are similar?

Show that they are equiangular Signup and view all the answers

What is the name of the theorem that states equiangular triangles are similar?

No specific name Signup and view all the answers

What is the advantage of using the equiangular triangles condition to prove similarity?

It only requires one condition to be true Signup and view all the answers

If two polygons are similar, what can be said about their corresponding sides?

They are in the same proportion Signup and view all the answers

What is the minimum number of sides required for two polygons to be similar?

No minimum number of sides Signup and view all the answers

If two triangles have proportional corresponding sides, what can be concluded about their areas?

Their areas are proportional Signup and view all the answers

If ∆ABC and ∆DEF are similar, what is the relationship between their corresponding angles?

They are equal Signup and view all the answers

What is the purpose of constructing GH in the proof of the theorem that triangles with proportional sides are similar?

To show that GH is parallel to BC Signup and view all the answers

What is the converse of the theorem that equiangular triangles are similar?

Triangles with proportional sides are similar Signup and view all the answers

If ∆ABC and ∆DEF are similar, what can be said about their corresponding heights?

They are proportional Signup and view all the answers

What is the condition for two triangles to be equiangular?

Equal corresponding angles Signup and view all the answers

If two triangles have equal corresponding heights, what can be concluded about their areas?

They are proportional Signup and view all the answers

What is the purpose of the proportionality theorem in the proof of the theorem that triangles with proportional sides are similar?

To establish proportionality of corresponding sides Signup and view all the answers

If two polygons are similar, which of the following statements is true?

Their corresponding sides are in the same proportion. Signup and view all the answers

What is the primary difference between congruent and similar polygons?

Congruent polygons have the same shape and size, while similar polygons have the same shape but differ in size. Signup and view all the answers

If ∆ABC is similar to ∆PQR, what can be said about the corresponding sides?

AB/BC = PQ/QR. Signup and view all the answers

What is the minimum number of conditions required to prove two triangles are similar?

One. Signup and view all the answers

Which of the following is NOT a necessary condition for two polygons to be similar?

They have the same shape but differ in size. Signup and view all the answers

What can be concluded about ∆ABC and ∆DEF if they have corresponding sides in the same proportion?

They are similar triangles. Signup and view all the answers

What is the purpose of the theorem that equiangular triangles are similar?

To provide an alternative way to prove two triangles are similar. Signup and view all the answers

If two triangles are similar, what can be said about their corresponding angles?

They are equal. Signup and view all the answers

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?

To prove that GH is parallel to BC Signup and view all the answers

What is the key concept used in the proof that triangles with sides in proportion are similar?

Proportionality of sides Signup and view all the answers

What is the conclusion that can be drawn if two triangles have corresponding sides in the same proportion?

The triangles are similar Signup and view all the answers

What is the necessary condition for two triangles to be similar?

The triangles have proportional corresponding sides Signup and view all the answers

What is the relationship between the areas of two similar triangles?

The areas are proportional to the squares of the corresponding sides Signup and view all the answers

What is the purpose of the proportionality theorem in the proof of the theorem that triangles with proportional sides are similar?

To prove that GH is parallel to BC Signup and view all the answers

What is the key concept used in the proof that equiangular triangles are similar?

Equiangularity of triangles Signup and view all the answers

What is the conclusion that can be drawn if two triangles are similar?

The triangles have proportional corresponding sides Signup and view all the answers

If two polygons have the same number of sides and are similar, what can be concluded about their corresponding angles?

They are equal Signup and view all the answers

What is the minimum requirement for two polygons to be similar?

They must have the same number of sides and proportional corresponding sides Signup and view all the answers

If ∆ABC and ∆DEF are similar, what can be said about their corresponding medians?

They are proportional Signup and view all the answers

What is the advantage of using the condition of equal corresponding angles to prove similarity?

It is more widely applicable Signup and view all the answers

If two triangles have proportional corresponding sides, what can be concluded about their corresponding altitudes?

They are proportional Signup and view all the answers

What is the primary difference between congruent and similar polygons?

Size Signup and view all the answers

If ∆ABC and ∆DEF are equiangular, what can be concluded about their corresponding sides?

They are proportional Signup and view all the answers

What is the purpose of the theorem that equiangular triangles are similar?

To provide an alternative method for proving similarity Signup and view all the answers

What is the main purpose of proving ∆AGH ∼ ∆ABC in the theorem that triangles with sides in proportion are similar?

To prove that ∆ABC is similar to ∆DEF Signup and view all the answers

What is the condition required to prove that two polygons are similar?

Corresponding sides are in the same ratio or corresponding angles are equal Signup and view all the answers

What is the advantage of using the theorem that triangles with sides in proportion are similar?

It allows us to prove similarity without showing equiangularity Signup and view all the answers

What is the relationship between the areas of ∆ABC and ∆DEF if ∆ABC ∼ ∆DEF?

The areas are in the same ratio as the corresponding sides Signup and view all the answers

What is the purpose of constructing Q on CA such that CQ = FD in the theorem that triangles with sides in proportion are similar?

To prove that CA / FD = CB / FE Signup and view all the answers

What can be concluded about ∆ABC and ∆DEF if ∆ABC ∼ ∆DEF and AB / DE = AC / DF?

The corresponding sides are in the same ratio Signup and view all the answers

What is the condition required to prove that two triangles are equiangular?

The corresponding angles are equal Signup and view all the answers

What is the main idea behind the proportionality theorem?

Triangles with equal heights have areas proportional to their bases Signup and view all the answers

Gr12 Mathematics: Ch 7.4 Similarity

Questions and Answers

What is the condition for two triangles to be similar according to the similarity conditions?

What can be concluded if two triangles have equal heights?

What is the definition of similar polygons?

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?

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 condition for two triangles to be equiangular?

What is the theorem that states equiangular triangles are similar?

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 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 is the required result to prove that two triangles are similar?

What is true about congruent polygons?

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?

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?

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 advantage of using the equiangular triangles condition to prove similarity?

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?

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?

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?

If ∆ABC and ∆DEF are similar, what can be said about their corresponding heights?

What is the condition for two triangles to be equiangular?

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?

If two polygons are similar, which of the following statements is true?

What is the primary difference between congruent and similar polygons?

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?

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 is the purpose of the theorem that equiangular triangles are similar?

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?

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 necessary condition for two triangles to be similar?

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 key concept used in the proof that equiangular 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?

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?

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?

What is the primary difference between congruent and similar polygons?

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 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 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 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 is the condition required to prove that two triangles are equiangular?

What is the main idea behind the proportionality theorem?

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