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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: ΔABC→ΔA'B'C'

Prove: ΔABC≅ΔA'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 ΔABC and ΔA'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 arΔABC=arΔA'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

For each transformation given:

  1. Plot the three points A0,4, B4,6, and C2,0, and their images A', B', and C' under the transformation.
  2. State whether the transformation appears to be an isometry.
  3. Find the pre image of 12,6.

G:x,y→-12x,-12y

Fold a piece of paper. Cut a design connecting the top and bottom point of the fold, as shown. Unfold the shape. Consider a mapping M of the points in the gray region to the corresponding points in the red region.

  1. Does M appear to be an isometry?
  2. If a point P is on line k, what is the image of P?
  3. If a point Q is not on line k, and MQ=Q', what is the relationship between the line k and QQ'→?

Repeat Exercise 26 but roll the ball off two walls.
  1. If f:x→x, find the images of -3, 6, and -6.
  2. Is f a one-to-one function? Explain.

Ois a point equidistant from parallel lines l1 and l2. A mapping M maps each point P of l1 to the point P' where PO→intersects l2.

  1. Is the mapping a one-to-one mapping of l1 and l2?
  2. Does this mapping preserve or distort distance?
  3. If l1 and l2 were not parallel, would the mapping preserve distance? Illustrate your answer with a sketch.
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