Question

In figure, AB = EF , BC = DE , AB is perpendicular to BD and EF is perpendicular to CE . Prove that triangle that ABD is congruent to triangle FEC .

Answer 1

Answer:

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Answer 2

Given: In figure, AB = EF , BC = DE , AB is perpendicular to BD and EF is perpendicular to CE.

To find: Prove that triangle that ABD is congruent to triangle FEC.

Solution:

The two triangles given in the figure are right-angled triangles. The perpendiculars of the triangles AB and EF are equal in length as mentioned in the question. The bases of the triangles are also equal in length. The angles B and E are the right angle of the right-angled triangles.

Since two sides and one angle of the two triangles are the same, we can say that the two triangles are congruent by SAS (Side Angle Side) postulate.

Therefore, the triangle that ABD is congruent to triangle FEC.