Question

tell if the triangles are congruent. if yes, write a congruence statement.
remember to be on the lookout for shared sides (reflexive property) and vertical angles
that are congruent to one another.
8.
9.
10.
11.
12.
13.

Explanation:

Step1: Analyze triangle congruence for problem 8

Check corresponding sides and angles. In \(\triangle EGI\) and \(\triangle QMO\), by Side - Angle - Side (SAS) congruence criterion (two sides and included angle).

Step2: Analyze triangle congruence for problem 9

Check \(\triangle RTV\) and \(\triangle YZX\). There is no congruence as side - side - angle (SSA) is not a valid congruence criterion.

Step3: Analyze triangle congruence for problem 10

For \(\triangle NPM\) and \(\triangle TRQ\), by Side - Side - Side (SSS) congruence criterion (all three sides equal).

Step4: Analyze triangle congruence for problem 11

In \(\triangle KNL\) and \(\triangle MLN\), by Angle - Side - Angle (ASA) congruence criterion (two angles and included side).

Step5: Analyze triangle congruence for problem 12

For \(\triangle DGE\) and \(\triangle FHE\), by Angle - Side - Angle (ASA) (vertical angles are equal, two sides and included angle).

Step6: Analyze triangle congruence for problem 13

In \(\triangle QPR\) and \(\triangle JLK\), by Angle - Side - Angle (ASA) (two angles and included side).

Answer:

1. \(\triangle EGI\cong\triangle QMO\) (by SAS)
2. No
3. \(\triangle NPM\cong\triangle TRQ\) (by SSS)
4. \(\triangle KNL\cong\triangle MLN\) (by ASA)
5. \(\triangle DGE\cong\triangle FHE\) (by ASA)
6. \(\triangle QPR\cong\triangle JLK\) (by ASA)