Question

State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used.

Answer 1

Answer:

Triangle OMN and Triangle OJK are similar by SAS Theorem

Step-by-step explanation:

we know that

The Side-Angle-Side (SAS) Similarity Theorem states that- If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles must be similar.

In this problem we have

∠JOK≅∠MON

The corresponding sides including the congruent angle are

OK and ON

OJ and OM

Verify if the corresponding sides are proportional

$\frac{OK}{ON}=\frac{OJ}{OM}$

substitute the given values

$\frac{21}{21+7}=\frac{33}{33+11}$

$\frac{21}{28}=\frac{33}{44}$

$21*44=33*28$

$924=924$ -----> is true

therefore

Triangle OMN and Triangle OJK are similar by SAS Theorem