If possible, draw an example of 2 noncongruent triangles that satisfy the following conditions. If not possible, then explain why.

Question

When six pairs of corresponding parts of two triangles are congruent, the triangles are congruent. If possible, draw an example of two noncongruent triangles that satisfy the following conditions. If not possible, then explain why.

a) three pairs of corresponding parts are congruent

b) four pairs of parts are congruent

c) five pairs of parts are congruent

Answer 1

Triangles 1 shows two similar triangles formed because of the parallel lines, so the large triangle and nested inner triangle have all three angles congruent, but the side lengths are different, so the triangles are not congruent.

Similarly Triangles 2 shows two similar triangles and one pair of sides congruent. But the sides are not in corresponding positions and the triangles are not congruent even though they have 4 congruencies.

Triangles 3 also has three congruencies: two sides and an angle, but they are not in corresponding positions.

For 5 congruencies we have to have 3 sides and 2 angles, or 2 sides and 3 angles. If 2 angles are congruent the third angle must also be congruent. And if all angles are congruent the two sides must include one of the angles, making the triangles congruent; so with 5 matching parts there will always be congruency.