Math Problem Statement

Mr. Jack used similar triangles to make a design.

Which statement about the triangles in the design must be true?

Select TWO correct answers. A.They are the same size but different shapes. B.They are the same size and shape. C.They are the same shape, but not necessarily the same size. D.They have corresponding sides that are congruent. E.They have corresponding angles that are congruent.

Solution

In similar triangles, the following two properties must always be true:

C. They are the same shape, but not necessarily the same size.
E. They have corresponding angles that are congruent.

Explanation:

  1. Similar triangles have the same shape but can differ in size, meaning their corresponding angles are equal, but their sides are proportional, not necessarily congruent.
  2. Corresponding angles in similar triangles are congruent, meaning they have the same measure.
  3. Corresponding sides of similar triangles are proportional, but not necessarily congruent (same length).

Let me know if you'd like a further breakdown or additional details on how this works!


Here are 5 questions to expand on this:

  1. What is the difference between congruent and similar triangles?
  2. How do you find the ratio of sides in similar triangles?
  3. Can all triangles with equal angles be classified as similar?
  4. How can we use proportions to solve for unknown sides in similar triangles?
  5. Are congruent triangles always similar? Why or why not?

Tip: Always remember that corresponding angles are congruent in similar triangles, but the corresponding sides are only proportional, not necessarily equal.

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Math Problem Analysis

Mathematical Concepts

Geometry
Similar Triangles

Formulas

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Theorems

Angle-Angle (AA) Similarity Theorem
Properties of Similar Triangles

Suitable Grade Level

Grades 6-8