Using Triangle Similarity Theorems

Question 1

Based on the side-splitter theorem, which side length would complete the proportion? StartFraction J M Over M K = StartFraction L N Over question mark EndFraction

Revolt · Accepted Answer

NK

Question 2

Question 2

Revolt · Accepted Answer

5.5

Question 3

Complete the statements to solve for x.

Revolt · Accepted Answer

By the converse of the side-splitter theorem, if JK/KL = , then KM ∥ JN.: NM/ML; Cross-multiply: (x – 5)() = x(x – 3).: x + 4; Multiply and simplify: x2 – x – = x2 – 3x.: 20; Solve for x: x = .: 10

Question 4

Complete the steps of the proof.

Revolt · Accepted Answer

✔ SAS similarity theorem; ♣:: SAS similarity theorem; ♦:: definition of similar triangles

Question 5

definition of congruent anglesX definition of corresponding angles✔ definition of similar triangles

Revolt · Accepted Answer

✔ definition of similar triangles

Question 6

Complete the statements to solve for x.

Revolt · Accepted Answer

✔ NM/ML; By the converse of the side-splitter theorem, if JK/KL = , then KM ∥ JN.: NM/ML; Cross-multiply: (x – 5)() = x(x – 3).: x + 4; Multiply and simplify: x2 – x – = x2 – 3x.: 20; Solve for x: x = .: 10

Question 7

x✔ x + 4X x – 3

Revolt · Accepted Answer

✔ x + 4

Question 8

X –19✔ 20

Revolt · Accepted Answer

✔ 20

Question 9

0.54.5✔ 10

Revolt · Accepted Answer

✔ 10

Question 10

Given that PO is a midsegment of △LMN, to which segment is MO congruent?

Revolt · Accepted Answer

OL

Using Triangle Similarity Theorems Answers

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