Question

Please help!!!
Which best explains the relationship between the two triangles below?

Answer 1

Its B

Explanation:

just took the test

Answer 2

1.
`\Delta ADC\sim \Delta RTS` because
`\angle A\cong \angle R`,
`\angle C\cong \angle S` and
`\angle D\cong \angle T`

Explanation:

We have been given two triangles
`\Delta ADC` and
`\Delta RTS`. We are asked to find the relationship between these triangles.

By angle sum property let us find measure of angle C of triangle ADC.

`m\angle C+m\angle D+m\angle A=180^(o)`

`m\angle C+51.2^(o)+96.5^(o)=180^(o)`

`m\angle C+147.7^(o)=180^(o)`

`m\angle C=180^(o)-147.7^(o)`

`m\angle C=32.3^(o)`

Let us find measure of angle T of triangle RTS.

`m\angle T+m\angle R+m\angle S=180^(o)`

`m\angle T+96.5^(o)+32.3^(o)=180^(o)`

`m\angle T+128.8^(o)=180^(o)`

`m\angle T=180^(o)-128.8^(o)`

`m\angle T=51.2^(o)`

We can see that
`m\angle C=m\angle S`,
`m\angle A=m\angle R` and
`m\angle D=m\angle T`. Therefore,
`\Delta ADC\sim \Delta RTS` and 1st option is the correct choice.