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Chapter 14: Q9. (page 574)

Explain how Corollary I follows from Theorem 14-1.

Short Answer

Expert verified

It verified that a triangle is mapped to a congruent triangle by isometry.

Step by step solution

01

Step 1. Given Information.

The theorem 14-1 states that an isometry maps a triangle to a congruent triangle.

Given: Isometry T: ΔABC→ΔA'B'C'

Prove: ΔABC≅ΔA'B'C'

Corollary 1 states that an isometry maps an angle to a congruent angle. It is also termed as angle isometry theorem corollary.

02

Step 2. Explanation.

According to theorem the two triangles ΔABC and ΔA'B'C' are congruent to each other. They are also isometric. So,

∠A=∠A'∠B=∠B'∠C=∠C'

Thus, all the three angles are mapped to congruent triangle.

03

Step 3. Conclusion.

Therefore, it verified that a triangle is mapped to a congruent triangle by isometry.

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Most popular questions from this chapter

Copy each figure on graph paper. Then draw the image by reflection in line k.

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