In the figure below, ΔABC ≅ ΔDEF. Point C is the point of intersection between and, while point E is the point of intersection between and. Prove ΔABC ∼ ΔGEC. (10 points)

As per AAA similarity postulate, the triangles ΔABC ∼ ΔGEC.

Step-by-step explanation:

We are given that the following triangles are congruent:

ΔABC ≅ ΔDEF

It means the corresponding angles will be equal to each other.

we can derive the following:

1.

2.  ...... (1)

3.

Now, let us look at the triangles ΔABC and ΔGEC. If we can prove that two of their angles are equal, we can prove that the triangles are similar.

1. because they are the vertically opposite angles.

2. In ΔDEF and ΔGEC, because they are the vertically opposite angles.

Using equation (1) above, we can derive that:

Two of the angles in ΔABC and ΔGEC are equal to each other so the third angle will also be equal i.e.

3.

Hence, by AAA similarity postulate, the triangles ΔABC ∼ ΔGEC.

the answer is 62