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Chapter 2: Q8 (page 45)

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

If EB鈫� is the bisector of 鈭�AEC, then m鈭�AEB=12m鈭�AEC .

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. EB鈫�bisects 鈭�AEC.

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 EB鈫�is the bisector 鈭�AEC, then m鈭�AEB=12鈭�AEC.

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

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Most popular questions from this chapter

Justify each statement with a property from algebra or property of congruence.

2a+b=2a+2b

Justify each statement with a property from algebra or property of congruence.

If AB炉鈮�CD炉and DC炉鈮�EP炉then AB炉鈮�EP炉.

If 鈭�Aand 鈭�Bare supplementary, find the value of x, m鈭�Aand m鈭�B.

25. role="math" m鈭�A=x+16,m鈭�B=2x-16

Mention what can be deduced from the given information.

Given: AE=DEand CE=BE

Justify each statement with a property from algebra or property of congruence.

If 5y=鈭�20then y=鈭�4.
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