Answer:
Therefore, the correct explanation is;
C. ∠L ≅ ∠L By Reflexive Prop. ≅.
Since
║
, ∠LOP ≅ ∠LMN by the Corr. ∠s Post. Therefore, ΔLOP ~ ΔLMN by AA ~. OP = 4 and MN = 8
Step-by-step explanation:
The given parameters are;
= 5
= 10
= 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;
/
=
/
= 5/10 = 1/2
∴ (x - 3)/(x + 1) = 1/2
2·(x - 3) = 1·(x + 1)
2·x - 6 = x + 1
2·x - x = 1 + 6 = 7
x = 7
= (x - 3) = 7 - 3 = 4
= 4
= x + 1 = 7 + 1 = 8
= 8
Therefore, the correct option is ∠L ≅ ∠L By Reflexive Prop. ≅.
Since
║
, ∠LOP ≅ ∠LMN by the Corr. ∠s Post. Therefore, ΔLOP ~ ΔLMN by AA ~. OP = 4 and MN = 8.