Gr12 Mathematics: Ch 7.4 Similarity
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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?

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

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

    <p>They are in the same proportion</p> Signup and view all the answers

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

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

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

    <p>One condition</p> Signup and view all the answers

    What is the condition for two triangles to be equiangular?

    <p>They have equal corresponding angles</p> Signup and view all the answers

    What is the theorem that states equiangular triangles are similar?

    <p>Theorem of Equiangular Triangles</p> Signup and view all the answers

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

    <p>∠AGH = ∠B</p> Signup and view all the answers

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

    <p>Theorem of Triangles with Sides in Proportion</p> Signup and view all the answers

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

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

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

    <p>They are proportional to their bases</p> Signup and view all the answers

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

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

    What is true about congruent polygons?

    <p>They are similar and have the same shape and size.</p> Signup and view all the answers

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

    <p>The same number of sides</p> Signup and view all the answers

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

    <p>Both conditions must be true for all polygons</p> Signup and view all the answers

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

    <p>They are equal</p> Signup and view all the answers

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

    <p>They are similar</p> Signup and view all the answers

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

    <p>Show that they are equiangular</p> Signup and view all the answers

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

    <p>No specific name</p> Signup and view all the answers

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

    <p>It only requires one condition to be true</p> Signup and view all the answers

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

    <p>They are in the same proportion</p> Signup and view all the answers

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

    <p>No minimum number of sides</p> Signup and view all the answers

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

    <p>Their areas are proportional</p> Signup and view all the answers

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

    <p>They are equal</p> 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?

    <p>To show that GH is parallel to BC</p> Signup and view all the answers

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

    <p>Triangles with proportional sides are similar</p> Signup and view all the answers

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

    <p>They are proportional</p> Signup and view all the answers

    What is the condition for two triangles to be equiangular?

    <p>Equal corresponding angles</p> Signup and view all the answers

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

    <p>They are proportional</p> 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?

    <p>To establish proportionality of corresponding sides</p> Signup and view all the answers

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

    <p>Their corresponding sides are in the same proportion.</p> Signup and view all the answers

    What is the primary difference between congruent and similar polygons?

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

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

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

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

    <p>One.</p> Signup and view all the answers

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

    <p>They have the same shape but differ in size.</p> Signup and view all the answers

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

    <p>They are similar triangles.</p> Signup and view all the answers

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

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

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

    <p>They are equal.</p> 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?

    <p>To prove that GH is parallel to BC</p> Signup and view all the answers

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

    <p>Proportionality of sides</p> Signup and view all the answers

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

    <p>The triangles are similar</p> Signup and view all the answers

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

    <p>The triangles have proportional corresponding sides</p> Signup and view all the answers

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

    <p>The areas are proportional to the squares of the corresponding sides</p> 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?

    <p>To prove that GH is parallel to BC</p> Signup and view all the answers

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

    <p>Equiangularity of triangles</p> Signup and view all the answers

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

    <p>The triangles have proportional corresponding sides</p> 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?

    <p>They are equal</p> Signup and view all the answers

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

    <p>They must have the same number of sides and proportional corresponding sides</p> Signup and view all the answers

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

    <p>They are proportional</p> Signup and view all the answers

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

    <p>It is more widely applicable</p> Signup and view all the answers

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

    <p>They are proportional</p> Signup and view all the answers

    What is the primary difference between congruent and similar polygons?

    <p>Size</p> Signup and view all the answers

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

    <p>They are proportional</p> Signup and view all the answers

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

    <p>To provide an alternative method for proving similarity</p> 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?

    <p>To prove that ∆ABC is similar to ∆DEF</p> Signup and view all the answers

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

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

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

    <p>It allows us to prove similarity without showing equiangularity</p> Signup and view all the answers

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

    <p>The areas are in the same ratio as the corresponding sides</p> 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?

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

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

    <p>The corresponding sides are in the same ratio</p> Signup and view all the answers

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

    <p>The corresponding angles are equal</p> Signup and view all the answers

    What is the main idea behind the proportionality theorem?

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

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