"Determine whether the triangles are similar. If so,..." solved and explained

High School
Geometry
High school geometry
Similarity

Kaycee Roche

Answered question

2021-02-03

Determine whether the triangles are similar.
If so, write a similarity statement and name the postulate or theorem you used. If not, explain.

Answer & Explanation

Daphne Broadhurst

Skilled2021-02-04Added 109 answers

Step 1 given
we have been given a triangle MNL in which P is a point on the side MN and O is the point on the side NL and OP is parallel ML
Step 2
first, we will take $△ N P O a n d △ N M L$
$∠ N = ∠ N$ (common angle)
$∠ N P O = ∠ N M L$ (corresponding angles as $O P | | M L$ )
so, the AA rule which states in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar.
$△ N M L \approx △ N P O$ (AA rule)
therefore the two triangles NML and NPO are similar.

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