Question

Can someone please help me with this (if you cant see it just zoom in)

Answer 1

Option A:
`(S R)/(B C)=(R T)/(C A)`

Option C:
`\angle R\cong \angle C`

Solution:

Given ΔRST similar to ΔABC.

To determine which statements are true for the given similarity triangles.

Option A:
`(S R)/(B C)=(R T)/(C A)`

By the similarity theorem,

If two triangles are similar, then the corresponding angles are equal and the corresponding sides are in the same ratio or proportion.

Therefore,
`(S R)/(B C)=(R T)/(C A)`

It is true.

Option B:
`\angle S\cong \angle A`

By the similarity theorem, corresponding angles are equal.

∠S is corresponding to ∠B.

So,
`\angle S\cong \angle B`.

That means ∠S is not corresponding to ∠A.

Therefore, it is false.

Option C:
`\angle R\cong \angle C`

By the similarity theorem, corresponding angles are equal.

∠R is corresponding to ∠C.

Therefore
`\angle R\cong \angle C`.

It is true.

Option D:
`(S R)/(B C)=(R T)/(AB)`

We already, proved in option A that
`(S R)/(B C)=(R T)/(C A).`

Therefore,
`(S R)/(B C)\\eq (R T)/(AB)`.

It is false.

Option A and Option C are true.

Hence
`(S R)/(B C)=(R T)/(C A)` and
`\angle R\cong \angle C`.