Question

Identify the correct explanation for why the triangles are similar. Then find TO and US.

Answer 1

/TO/ and /US/ are parallel so the angles at TOS (©)and the external angle at OSU (©) are equal ( Z angles) therefore the internal angle at OSU will be 180 - © similarly the angle at POT is also 180 - ©

Answer 2

The correct explanation is option B;

B. ∠L ≅ ∠L By Reflexive Prop. ≅.

Since ║ , ∠LOP ≅ ∠LMN by the Corr. ∠s Post. Therefore, ΔLOP ~ ΔLMN by AA ~. OP = 2 and MN = 6

Explanation:

The given parameters are;

= 5

= 10

= + = 15

= x - 3

= x + 1

A two column proof is presented as follows;

Statement Reason

∠L ≅ ∠L By Reflexive property of congruency

║ Given

∠LOP ≅ ∠LMN By the Corresponding angles Postulate

Therefore

ΔLOP ~ ΔLMN By AA similarity Postulate

Where we have that ΔLOP and ΔLMN, we get;

/ = / = 5/15 = 1/3

∴ (x - 3)/(x + 1) = 1/3

3·(x - 3) = 1·(x + 1)

3·x - 9 = x + 1

3·x - x = 1 + 9 = 10

2·x = 10

x = 10/2 = 5

x = 5

= (x - 3) = 5 - 3 = 2

= 2

= x + 1 = 5 + 1 = 6

= 6

Therefore, the correct option is ∠L ≅ ∠L By Reflexive Prop. ≅.

Since ║ , ∠LOP ≅ ∠LMN by the Corr. ∠s Post. Therefore, ΔLOP ~ ΔLMN by AA ~. OP = 2 and MN = 6.