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Chapter 2: Q21. (page 59)

Can you conclude from the information given for the exercise that XY→⊥XZ→?

m∠1=m∠4

Short Answer

Expert verified

The relation between the provided lines cannot be concluded.

Step by step solution

01

Step 1. Definition of congruent angles.

Angles having the same measurement are referred as the congruent angles.

02

Step 2. Definition of perpendicular lines.

The definition of perpendicular lines states that the relation between two lines is perpendicular when the measurement of angles formed by those lines is equal to 90°.

03

Step 3. Make the conclusion.

The definition of perpendicular line does not match with the relation between the provided angles because the measurement is not given. So the relation between the provided lines cannot be concluded.

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Most popular questions from this chapter

Copy everything shown and write a two-column proof.

Given:RQ=TP;

ZQ=ZP

Prove:RZ=TZ

Prove the following statement by filling in the blanks.

If A and B have coordinated a and b, with b>a, and the midpoint M of AB¯ has coordinate x, then prove x=a+b2.

Proof:

Statement

Reasons

1. A, M, and B have coordinated a, x, and b respectively; b>a.

1. ?

2. AM=x−a;MB=b−x

2. ?

3. M is the midpoint of AB¯.

3. ?

4. AM¯≅MB¯, orAM=MB

4. ?

5.x−a=b−x

5. ?

6. 2x=?

6. ?

7. x=a+b2

7. ?

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Provide a counterexample to show that each statement is false. You may use words or draw a diagram.

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