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Chapter 14: Q10. (page 574)

Explain how Corollary 2 follows from Theorem 14-1.

Short Answer

Expert verified

It verified that a polygon to a polygon of same area is mapped 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: 螖ABC鈫�螖A'B'C'

Prove: 螖ABC鈮�螖A'B'C'

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.

02

Step 2. Explanation.

According to theorem the two triangles 螖ABC and 螖A'B'C' are congruent to each other and isometric. If two triangles are congruent to each other as per the theorem, then their areas such as ar螖ABC=ar螖A'B'C', two triangle are mapped to congruent triangle thus have equal areas.

03

Step 3. Conclusion.

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

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Most popular questions from this chapter

When the word HIDE is reflected in a horizontal line, the image is still HIDE. Can you think of the other words that are unchanged when reflected in a horizontal line?

Write the coordinates of the image of each point by reflection in,

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Consider the mapping S:x,y鈫�x,0.

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Write the coordinates of the image of each point by reflection in,

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