Chapter 14: Q20. (page 580)

In Exercise 18-20, refer to the diagrams om page 578. Given the reflection $R_{m} : \vec{P Q} \to \vec{P' Q'}$ , write the key steps of a proof that $P Q = P' Q'$ for each case.
Case 4.

Short Answer

Expert verified

It is proved that, $P Q = P' Q'$ .

Step by step solution

Step 1. Given Information.

It is given that $\bar{P' Q'}$ is reflection of PQ in line m.

Step 2. Proof.

Since, $\bar{P' Q'}$ is reflection of PQin line m and it is visible in the figure that P and Q are not on the line m hence, m is perpendicular bisector of $P P' and Q Q'$ .

And if m is perpendicular bisector of both $P P' and Q Q'$ . Since, $P P' and Q Q'$ are not on same line then it obvious that $P P' and Q Q'$ are parallel.

The two statements that m is perpendicular bisector of $P P' and Q Q'$ , $P P'$ is parallel to $Q Q'$ leads to conclude that $P Q = P' Q'$ .

Step 3. Conclusion.

It is proved that, $P Q = P' Q'$ .

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In Exercise 18-20, refer to the diagrams om page 578. Given the reflection $R_{m} : \vec{P Q} \to \vec{P' Q'}$ , write the key steps of a proof that $P Q = P' Q'$ for each case.
Case 4.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Proof.

Step 3. Conclusion.

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In Exercise 18-20, refer to the diagrams om page 578. Given the reflection Rm:PQ→→P'Q'→, write the key steps of a proof that PQ=P'Q' for each case.Case 4.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Proof.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Theoretical and Mathematical Physics

Mechanics Maths

Pure Maths

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Exercise 18-20, refer to the diagrams om page 578. Given the reflection $R_{m} : \vec{P Q} \to \vec{P' Q'}$ , write the key steps of a proof that $P Q = P' Q'$ for each case.
Case 4.