Question

If JO = 32 is JKO = PMN? If so, find JN

A. Yes, JKO = PMN by AAS; JN = 32
B. Yes, JKO = PMN by AAS; JN = 51.
C. Yes, JKO = PMN by SAS; JN = 51.
D. No, the triangles are not congruent.

(the answer is not C)

Answer 1

The answer is B. Yes, JKO = PMN by AAS; JN = 51.

Answer 2

Option B.

Explanation:

Given information: JO = 32, JK║PM, KO║MN.

In triangle JKO and PMN,

`\angle JOK\cong \angle PNM` (Corresponding angles)

`\angle OJK\cong \angle NPM` (Corresponding angles)

`JK\cong PM` (10+15=25)

Two angles and one non-include side are congruent to corresponding two angle and non-included side.

`\triangle JKO\cong \triangle PMN` (By AAS postulate)

Corresponding parts of congruent triangles are congruent.

`JO\cong PN` (CPCTC)

`JO=PN` (Definition of congruent segment)

`JO=PO+ON`

`32=13+ON`

`32-13=ON`

`19=ON`

We need to find the value of JN.

`JN=JO+ON`

`JN=32+19`

`JN=51`

Therefore, the correct option is B.