Question

Given AC ≅ FE and CB ≅ ED which statement is correct?

Angle A is larger than angle B.

Angle C is congruent to angle E.

Angle C is smaller than angle E.

Angle C is larger than angle E.

Answer 1

D. C is smaller than E

Explanation:

Answer 2

Answer: The correct option is

(D) Angle C is larger than angle E.

Step-by-step explanation: Given that in triangles ABC and DEF,

AC ≅ FE and CB ≅ ED.

We are to select the correct statement from the given options.

We have the following inequality theorem.

SSS Inequality Theorem : If two sides of a triangle are congruent to two sides of another triangle, but the third side of the first triangle is longer than the third side of the second triangle, then the included angle of the first triangle is greater in measure than the included angle of the second triangle.

In ΔABC and ΔDEF,

the sides BC and AC are congruent to the sides DE and EF respectively,

but AB = 15 in. and DF = 11 in.

That is, AB > DF.

Therefore, the included angle C in ΔABC > the included angle E in ΔDEF.

Thus, angle C is larger than angle E.

Option (D) is correct.