To name: Which of the theorems can be used to prove triangles are congruent.
Answer to Problem 30E
Two theorems are SSS Congruence Theorem and SAS Congruence Theorem.
Explanation of Solution
Given information:
Formula used:
Side-Side-Side Congruence Theorem
If three sides of one triangle are congruent to three sides of a second triangle, then two triangles are congruent.
Side-Angle-Side Congruence Theorem
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then two triangles are congruent.
Calculation:
The two theorems that can be used to prove the triangles are congruent are :-
1. Side- Side-Side Congruence Theorem
2. Side-Angle-Side Congruence Theorem
As either all sides can be equal or the angle included in the sides be equal.
Hence, two theorems are SSS Congruence Theorem and SAS Congruence Theorem.
Chapter 12 Solutions
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