Question

DIRECTIONS: 1-16 State whether triangles are congruent using: SSS, SAS, NC If congruent, WRITE CONGRUENCE STATEMENT

Answer 1

To determine whether triangles are congruent, we use criteria such as SSS (Side-Side-Side), SAS (Side-Angle-Side), and NC (No Criteria). SSS means that the three sides of one triangle are equal to the three sides of another triangle. SAS means that two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle. NC is used when no criteria can be applied to determine congruence.

Step-by-step explanation:

When determining whether triangles are congruent, we use different criteria such as SSS (Side-Side-Side), SAS (Side-Angle-Side), and NC (No Criteria). Let's go through each criterion:

1. SSS: If the three sides of one triangle are equal to the three sides of another triangle, then the triangles are congruent. For example, if triangle ABC has sides of lengths 5, 6, and 7, and triangle DEF has sides of lengths 5, 6, and 7, we can say that triangle ABC is congruent to triangle DEF using the SSS criterion.
2. SAS: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent. For example, if triangle ABC has sides of lengths 5, 7, and an angle of 60 degrees, and triangle DEF has sides of lengths 5, 7, and an angle of 60 degrees, we can say that triangle ABC is congruent to triangle DEF using the SAS criterion.
3. NC: If no criteria can be applied to determine congruence, we state that the triangles are not congruent.