In triangle ABC, angle A = 30°, angle B = 40° and angle C = 110° and In triangle PQR, angle P = 30°, angle Q = 40°, angle R = 110°. A student says that triangle ABC is Congruent to triangle PQR by AAA (Angle Angle Angle) congruence criterion. Is he Justified. WHY or WHY NOT.
Answers
Answer:
They are not congruent. They are identical triangles.
Step-by-step explanation:
Two triangles with same set of angles do not look same in size.
For example, Take 2 equilateral triangles of side 3cm and 10cm.
Both have 3 sets of equal angles. i.e. corresponding angles are same for both the triangles.
But they are of different size. (Lengths of sides are different).
So they are not congruent. They are called identical triangles.
Along with 3 angles, if any of side of one triangle are same, then it is congruent. (Side opposite to same angle)
In the given example, both triangles are having same set of angles. But it is not mentioned about the sides of the triangle.
Hence we cannot derive congruency.
They are identical triangles.
answer is in above
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