Question

Two triangles are shown below. Which statement is sufficient to prove that AACB ~ARTS ? AB AC 1 BA BC CA TR LA ZR, ZB ZT AC RT 1 AB RS 6 RT RS SR ST

Answer 1

For both triangles to be similar, the corresponding sides of both triangles are always in the same ratio.

So for the corresponding sides:

1) BA ans SR, the ratio will be

$\frac{BA}{SR}$

2)AC and RT, the ratio will be

$\frac{AC}{RT}$

3) BC and ST, the ratio will be

$\frac{BC}{ST}$

As mentioned above, the ratio between corresponding sides is always the same so that, if the triangles are simmilar the we know that:

$\frac{AB}{RS}=\frac{BC}{ST}=\frac{AC}{RT}$

The correct option is the first one.