Question

for each of the following conditions, is it possible to construct two noncongruent triangles? explain why or why not.
a. a triangle with angles measuring 60° and 70° and an included side of 8 in.
b. a triangle with angles measuring 60° and 70° and a non - included side of 8 cm on a side of the 60° angle.
c. a triangle with angles measuring 30°, 70°, and 80°
a. choose the correct answer below.
a. it is not possible, because any two triangles with these conditions are congruent by aas.
b. it is not possible, because any two triangles with these conditions are congruent by sas.
c. it is not possible, because any two triangles with these conditions are congruent by asa.
d. it is possible, because the given conditions determine a unique shape but not size.

Explanation:

Step1: Recall congruence postulates

We know ASA (Angle - Side - Angle) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the two triangles are congruent.

Step2: Analyze given conditions

In part a, we have two angles ($60^{\circ}$ and $70^{\circ}$) and their included side of length 8 in. This satisfies the ASA congruence postulate.

Answer:

C. It is not possible, because any two triangles with these conditions are congruent by ASA.