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 shape, but not necessarily the same size.

B.They are the same size but different shapes.

C.They have corresponding sides that are congruent.

D.They are the same size and shape.

E.They have corresponding angles that are congruent.

Solution

The concept of similar triangles means that they are the same shape, but not necessarily the same size. Additionally, corresponding angles in similar triangles are always congruent, and their corresponding sides are proportional, but not necessarily congruent.

Therefore, the TWO correct answers are:

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

Would you like further details or have any questions?

Here are 5 related questions to expand on this:

  1. How do you prove two triangles are similar?
  2. What is the difference between congruent triangles and similar triangles?
  3. Can two triangles be similar if only two of their angles are congruent?
  4. How do you use proportions to solve for missing sides in similar triangles?
  5. What is the role of the scale factor in similar triangles?

Tip: In geometry, always check for angle congruence and side proportionality when determining if triangles are similar.

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Math Problem Analysis

Mathematical Concepts

Geometry
Similar Triangles
Congruence
Proportionality

Formulas

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Theorems

Angle-Angle (AA) Similarity
Corresponding Angles Postulate

Suitable Grade Level

Grades 8-10