Question

Explain how Corollary I follows from Theorem 14-1.

Short answer

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

Step-by-step solution

Step 1. Given Information.

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

Given: Isometry T: $\Delta ABC\to \Delta A\text{'}B\text{'}C\text{'}$

Prove: $\Delta ABC\cong \Delta A\text{'}B\text{'}C\text{'}$

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

Step 2. Explanation.

According to theorem the two triangles $\Delta ABC$ and $\Delta A\text{'}B\text{'}C\text{'}$ are congruent to each other. They are also isometric. So,

$\begin{array}{l}\angle A=\angle A\text{'}\\ \angle B=\angle B\text{'}\\ \angle C=\angle C\text{'}\end{array}$

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

Step 3. Conclusion.

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