Question

Geometry- Question #8a) none of the the optionsb) Triangle DEG is not congruent to triangle FGEFGEc) Triangle DEG is congruent to triangle FGE ; all corresponding sides and angles are congruent.

Answer 1

Answer:

Option C:

Triangle DEG is congruent to triangle FGE ; all corresponding sides and angles are congruent.

Explanation:

The rectangle DEFG is divided into two triangles. That is △DEG and △FGE

From the diagram shown:

DE ≅ GF

DG ≅ EF

Note that the two sides EF and GF with an included < F in △FGE are equal to DE and DG with an included △DEG.

The SAS rule states that two triangles are congruent if two sides and an included angle of one is equal to the corresponding two sides and an included angle of the other

Therefore, the two triangles △DEG and △FGE are congruent by the Side-Angle-Side rule of congruence (SAS rule)