Question

Explain how Corollary 2 follows from Theorem 14-1.

Short answer

It verified that a polygon to a polygon of same area is mapped 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 2 states that an isometry maps a polygon to a polygon with the same area. It is also termed as polygon 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 and isometric. If two triangles are congruent to each other as per the theorem, then their areas such as $\text{ar}\left(\Delta ABC\right)=\text{ar}\left(\Delta A\text{'}B\text{'}C\text{'}\right)$, two triangle are mapped to congruent triangle thus have equal areas.

Step 3. Conclusion.

Hence, it verified that a polygon to a polygon of same area is mapped by isometry.