Chapter 14: Q18. (page 580)

In Exercise 18-20, refer to the diagrams on 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 2.

Short Answer

Expert verified

The required proof is as shown in the below steps.

Step by step solution

Step 1. Given Information.

Given the reflection $R_{m} = \bar{P Q} \to \bar{P' Q'}$ and the diagram,

Step 2. Formula Used.

Definition of reflection.

Step 3. Proof.

In the given reflection through m $P = P'$

And Q has a reflection $Q'$ so from the definition of reflection we know that $\bar{Q Q'} ⊥ m$ and, Q and $Q'$ are equidistance from line m, and let O be the intersection of $\bar{Q Q'}$ and m.

Here

$P O$ is common, $∠ P O Q = ∠ P O Q'$ and $O Q = O Q'$

Hence $Δ P O Q \tilde{=} Δ P O Q'$ .

Now as the triangle are congruent, it can be concluded that $P Q = P' Q'$ .

Therefore, $P Q = P' Q'$ is proved.

Step 4. Conclusion.

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

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In Exercise 18-20, refer to the diagrams on 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 2.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Formula Used.

Step 3. Proof.

Step 4. Conclusion.

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In Exercise 18-20, refer to the diagrams on page 578. Given the reflection Rm:PQ→→P'Q'→, write the key steps of a proof that PQ=P'Q'for each case.Case 2.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Formula Used.

Step 3. Proof.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Decision Maths

Calculus

Geometry

Logic and Functions

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In Exercise 18-20, refer to the diagrams on 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 2.