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Chapter 2: Q7 (page 45)

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

If EB炉bisects AF炉, then E is the midpoint of AF炉 .

Short Answer

Expert verified

The midpoint 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 point E.

02

Step 2. State the midpoint theorem.

The theorem states that the line segment formed by joining the midpoints of the two sides of a triangle is parallel and also half of the length of the third side of the triangle.

03

Step 3. State the conclusion.

As EB炉bisects AF炉 at the point E, so, E is the midpoint of AF炉.

Therefore, the statement about the diagram is justified by the midpoint theorem.

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Most popular questions from this chapter

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

If , then B is the midpoint of .

Copy everything shown and write a two-column proof.

Given:m鈭�1=m鈭�2;

m鈭�3=m鈭�4;

Prove:m鈭�SRT=m鈭�STR

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

If D is the midpoint of BC炉, then BD=12BC.

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炉 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鈭�a;MB=b鈭�x

2. ?

3. M is the midpoint of AB炉.

3. ?

4. AM炉鈮�MB炉, orAM=MB

4. ?

5.x鈭�a=b鈭�x

5. ?

6. 2x=?

6. ?

7. x=a+b2

7. ?

Justify each step.

23b=8鈭�2b

2b=38鈭�2b

2b=24鈭�6b

8b=24

b=3
See all solutions

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