Subjects geometry

Triangle Congruence 2Bf2Ad

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

Question: Given that the triangles are congruent by the SSS congruence theorem, which of the following is a valid congruence statement? △ZAB≅△CLD △ZAB≅△CDL △AZB≅△CDL None of these
1. **State the problem:** We have two triangles, △AZB and △CDL, with sides marked by ticks indicating congruent sides. 2. **Identify the vertices and sides:** - Triangle △AZB has vertices A (top-left), Z (bottom-left), and B (center-right). - Triangle △CDL has vertices C (top-left), D (top-right), and L (bottom-right). 3. **Match sides by ticks:** - Side AZ has one tick, matching side CD with one tick. - Side AB has two ticks, matching side DL with two ticks. - Side ZB has three ticks, matching side CL with three ticks. 4. **SSS congruence theorem:** If all three sides of one triangle are congruent to the corresponding three sides of another triangle, the triangles are congruent. 5. **Determine the correct vertex correspondence:** - Since AZ corresponds to CD, vertex A corresponds to C, and vertex Z corresponds to D. - Since AB corresponds to DL, vertex B corresponds to L. 6. **Write the congruence statement with correct order:** - The triangle △AZB corresponds to △CDL. 7. **Answer:** - The valid congruence statement is $$\triangle AZB \cong \triangle CDL$$. **Final answer:** $$\triangle AZB \cong \triangle CDL$$
A Z B | || ||| C D L | || |||