Consider any isosceles triangle. Notice that by changing the angle between the congruent sides you will obtain a another isosceles triangle that satisfies the given condition. Are these two triangles congruent?
False
Practice makes perfect
We want to determine if the following statement is true or false.
Congruent sides in an isosceles triangle are called the legs. To determine if the statement is true, we need to decide if a pair of two isosceles triangle with equal legs is always congruent. Let's consider the following isosceles triangle.
Next, we will change the measure of ∠ A. This will give us a new triangle PQR. The legs of the triangle also measure 2.2 units, but the angle between the legs is now 100^(∘).
We can see that the congruent sides in the first isosceles triangle have the same measure as the congruent sides in the other triangle. Because the angles between the legs are different, △ ABC is not congruent to △ PQR.
△ ABC ≆ △ PQR
We found a counterexample to the statement. Therefore, the given statement is false.
