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Chapter 2: Q9 (page 45)

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

If ∠BEC≅∠CEF, thenEC→ is the bisector of ∠BEF .

Short Answer

Expert verified

The angle bisector theorem justifies the statement about the diagram.

Step by step solution

01

Step 1. Observe the given diagram.

The diagram constitutes a straight-line AEF and two other lines meet the line AEF at the point E. EC→ bisects ∠BEF.

02

Step 2. State the angle bisector theorem.

The relative lengths of the two parts in which the side of a triangle is separated by a line bisecting the opposite angle. This equates their relative lengths with the relative lengths of the triangle's other two sides.

03

Step 3. State the conclusion

Considering the given diagram and the statement that if ∠BEC≅∠CEF, then EC→is the bisector ∠BEF.

Therefore, the statement about the diagram is justified by the angle bisector theorem.

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Most popular questions from this chapter

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.

n>5only if n>7.

State the converse of each conditional. Is the converse true or false?

If , then .

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.

Copy everything shown and write a two-column proof.

Given: RP=TQ;

PS=QS

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