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Chapter 2: Q20. (page 59)

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

∠2≅∠3

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

Mention what can be deduced from the given information.

Given: AC¯bisects DB¯

DB¯bisects AC¯

CE=BE

State which postulate, definition, or theorem justifies the statement about the diagram.

If D is the midpoint of BC¯, then BD¯≅DC¯.

Consider the following statements:

Reflexive Property: Robot A is as rusty as itself.

Symmetric Property: If Robot A is as rusty as Robot B, then Robot B is as rusty as Robot A.

Transitive Property: If Robot A is as rusty as Robot B and Robot B is as rusty as Robot C, then Robot A is as rusty as Robot C.

A relation such as “is as rusty as” that is reflexive, symmetric, and transitive is an equivalence relation. Which of the following are equivalence relations?

a. Is rustier than

b. Has the same length as

c. Is opposite (for rays)

d. Is coplanar with (for lines)

Prove the following statements by filling in the blanks.

Given: BX→is the bisector of ∠ABC

Proof:

Statement

Reasons

1. BX→is the bisector of ∠ABC

1. ?

2. ∠ABX≅?, or m∠ABX=?

2. ?

3. m∠ABX+m∠XBC=m∠ABC

3. ?

4. m∠ABX+m∠ABX=m∠ABC, or2m∠ABX=m∠ABC

4. ?

5. m∠ABX=12m∠ABC

5. ?

6.m∠XBC=12m∠ABC

6. Substitution Prop. (Steps ? and ?)

Provide a counterexample to show that each statement is false.

Statement: If a four-sided figure has four right angles, then it has four congruent sides.
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