Gr 10 Math Ch 4: Simularity of Triangles
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Questions and Answers

Which condition must be met for two triangles to be considered similar?

  • They must have the same angles. (correct)
  • They must have equal areas.
  • They must be the same size.
  • They must have proportionate side lengths.

    • If triangles are similar, what can be deduced about their corresponding sides?

  • They are all the same size.
  • They are proportional to one another. (correct)
  • They are equal in length.
  • They have a constant ratio that varies with size.

    • What is the ratio of the sides in a triangle with angles of 30°, 60°, and 90°?

  • 1:2:3
  • 2:1:$ rac{1}{2}$
  • 1:$ rac{ oot{3}}{2}$:1 (correct)
  • 1:$ rac{ oot{2}}{2}$:$ rac{3}{2}$

    • Which of the following statements about the order of vertices in similar triangles is true?

    <p>The order must reflect corresponding angles.</p> Signup and view all the answers

    In similar triangles $ riangle ABC$ and $ riangle DEF$, what is true about angles A, B, and C?

    <p>They are equal to the angles D, E, and F respectively.</p> Signup and view all the answers

    What must be true for two triangles to have proportional sides?

    <p>They have the same angles.</p> Signup and view all the answers

    Which of the following ratios represents the equality in corresponding sides of similar triangles?

    <p>$ rac{AB}{DE} = rac{BC}{EF}$</p> Signup and view all the answers

    What happens to the ratio of corresponding side lengths if the angle remains constant in similar triangles?

    <p>The ratio will remain constant.</p> Signup and view all the answers

    Which of the following properties is true for similar triangles?

    <p>The ratios of corresponding sides are constant.</p> Signup and view all the answers

    In similar triangles, if one pair of sides is proportional, what can be inferred about the other pairs?

    <p>Other pairs must also be proportional.</p> Signup and view all the answers

    If triangle ABC is similar to triangle DEF, what relationship holds between the angles?

    <p>Angle B is equal to angle E.</p> Signup and view all the answers

    What is the consequence of not maintaining the correct order of vertices when labeling similar triangles?

    <p>The corresponding sides may be incorrectly matched.</p> Signup and view all the answers

    Which of the following ratios is consistent for similar triangles with corresponding sides?

    <p>$ rac{AB}{AC} = rac{DE}{DF}$</p> Signup and view all the answers

    When comparing triangle ABC with triangle GHK, which statement about their corresponding angles is accurate?

    <p>Angle A is equal to angle G.</p> Signup and view all the answers

    What relationship exists between the areas of similar triangles, such as ABC and DEF?

    <p>The area ratio is equal to the square of the side length ratio.</p> Signup and view all the answers

    Which of these must be true for triangles to be similar?

    <p>They must have two equal angles.</p> Signup and view all the answers

    In the context of similar triangles, if triangle ABC is similar to triangle DEF, which of the following must be true?

    <p>The ratio of corresponding sides is equal.</p> Signup and view all the answers

    Which of the following describes the relationship between the angles of similar triangles?

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

    What does the notation $ \Delta ABC \sim \Delta DEF $ imply about the triangles?

    <p>The order of vertices indicates which sides are proportional.</p> Signup and view all the answers

    If triangle ABC has side lengths in the ratio 3:4:5, what would be the corresponding sides of a similar triangle DEF with a ratio of 6:8:10?

    <p>The sides of triangle DEF are double that of triangle ABC.</p> Signup and view all the answers

    Which of the following scenarios correctly demonstrates the properties of similar triangles?

    <p>Two triangles with angles of 30°, 60°, and 90° that have identical ratios.</p> Signup and view all the answers

    What assumption can be made about the lengths of corresponding sides when comparing two similar triangles?

    <p>They will vary but will maintain proportional ratios.</p> Signup and view all the answers

    When two triangles are similar, what can be concluded about their corresponding sides and angles?

    <p>All corresponding angles are equal and corresponding sides are proportional.</p> Signup and view all the answers

    If two triangles have corresponding angles of 45°, 45°, and 90°, which of the following statements is true about their side lengths?

    <p>The side lengths will vary but maintain a constant ratio.</p> Signup and view all the answers

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