Question

PLEASE HELP ME ASAP!! I NEED ANSWERS AND EXPLANATIONS FAST!!!

Answer 1

d.
`\angle BIJ \cong \angle CGJ\ and\ \angle BJI \cong \angle CJG`

Explanation:

Here, we are given a diagram in which there are two triangles to be considered:

`\triangle CJG \ and\ \triangle BJI`.

We can consider the whole diagram in the form as attached in the answer area.

To find:

The conditions to prove
`\triangle CJG \sim \triangle BJI`.

Solution:

First of all, let us learn about AAA similarity.

AAA stands for Angle Angle Angle.

i.e. when we prove that the all the three corresponding angles of two triangles are equal ,the triangles are similar.

There is one more property of the triangles, that if two angles of two triangles are equal then the third angle of the triangles will also be equal to each other.

So, actually, to prove that
`\triangle CJG \sim \triangle BJI`, we need the conditions that two corresponding angles of the triangles are equal to each other, then we can say that third angle will also be equal. Therefore the triangles will be similar to each other.

Let us consider the corresponding angles:

`\angle BIJ \ and \ \angle CGJ\ ,\ \angle BJI \ and \ \angle CJG\ , \ \angle IBJ\ and \ \angle GCJ`

So, if we are given that any of the two above three pairs are equal/congruent to each other, we can prove
`\triangle CJG \sim \triangle BJI`.

Therefore, the correct answer is:

d.
`\angle BIJ \cong \angle CGJ\ and\ \angle BJI \cong \angle CJG`