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Chapter 2: Q9 (page 45)

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

If 鈭�BEC鈮�鈭�CEF, thenEC鈫� is the bisector of 鈭�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鈫� bisects 鈭�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 鈭�BEC鈮�鈭�CEF, then EC鈫�is the bisector 鈭�BEF.

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

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Most popular questions from this chapter

Write a definition of congruent angles as a biconditional.

Write each biconditional as two conditionals that are converses of each other.

Points lie in one plane if and only if they are coplanar.

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

m鈭�AEB+m鈭�BEF=180

State the number that is paired with the bisector of 鈭�CDE.

State the hypothesis and the conclusion of each conditional.

only if
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