Question

In the following triangle, point OOO is the midpoint of \overline{LM}
LM
start overline, L, M, end overline, and point PPP is the midpoint of \overline{LN}
LN
start overline, L, N, end overline.

Below is the proof that \overline{OP}\parallel\overline{MN}
OP
∥
MN
start overline, O, P, end overline, \parallel, start overline, M, N, end overline. The proof is divided into four parts, where the title of each part indicates its main purpose.
Complete part A of the proof.
Part A: Prove \dfrac{LM}{LO} = 2
LO
LM
​
=2start fraction, L, M, divided by, L, O, end fraction, equals, 2
Statement Reason
1 LO=OMLO=OML, O, equals, O, M Definition of midpoint
2 LM=LO+LM=LO+L, M, equals, L, O, plus

Segment addition postulate
3 LM=LO+LM=LO+L, M, equals, L, O, plus

Substitution (1, 2)
4 \dfrac{LM}{LO}=
LO
LM
​
=start fraction, L, M, divided by, L, O, end fraction, equals

Answer 1

Answer:

In the following triangle, point OOO is the midpoint of \overline{LM}

LM

start overline, L, M, end overline, and point PPP is the midpoint of \overline{LN}

LN

start overline, L, N, end overline.

Below is the proof that \overline{OP}\parallel\overline{MN}

OP

∥

MN

start overline, O, P, end overline, \parallel, start overline, M, N, end overline. The proof is divided into four parts, where the title of each part indicates its main purpose.

Complete part D of the proof.

Part A: Prove \dfrac{LM}{LO} = 2

LO

LM

​

=2start fraction, L, M, divided by, L, O, end fraction, equals, 2

[Show the steps.]

Part B: Prove \dfrac{LN}{LP} = 2

LP

LN

​

=2start fraction, L, N, divided by, L, P, end fraction, equals, 2

[Show the steps.]

Part C: Prove \triangle LMN\sim \triangle LOP△LMN∼△LOPtriangle, L, M, N, \sim, triangle, L, O, P

[Show the steps.]

Part D: Prove \overline{OP}\parallel\overline{MN}

OP

∥

MN

start overline, O, P, end overline, \parallel, start overline, M, N, end overline

Statement Reason

12

Measures of corresponding

of similar triangles are

. (Part C)

13 \overline{OP}\parallel\overline{MN}

OP

∥

MN

start overline, O, P, end overline, \parallel, start overline, M, N, end overline If a transversal crosses two lines and corresponding angles are congruent, then the lines are parallel. (12)

Step-by-step explanation: