Two triangles and satisfy the following conditions: .

MATHEMATICS · Multi-part · CBSE · Mathematics · Triangles · Triangles

Problem

Two triangles △ABC\triangle ABC and △DEF\triangle DEF satisfy the following conditions: AB=DE=5 cm,  BC=DF=7 cm,  ∠A=∠D=50∘AB = DE = 5\ \text{cm},\; BC = DF = 7\ \text{cm},\; \angle A = \angle D = 50^{\circ}. (i) Is the above information sufficient to prove that the two triangles are congruent? If not, identify one additional statement (only one) that would make the congruence certain. (ii) Suppose it is further known that AC=EFAC = EF. Prove that △ABC≅△DEF\triangle ABC \cong \triangle DEF. (iii) From the result in part (ii), state which two angles of the triangles must be equal and justify your statement.

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