Question

Please help me understand how to do this!

In ΔRST shown below, segment SU is an altitude:

What property or definition is needed to prove that ΔRUS is similar to ΔSUT?

Answer 1

it would be answer choice 3

Answer 2

The correct option is 1.

Explanation:

It is given that in ΔRST , segment SU is an altitude. It means the angle SUR and angle SUT are right angles.

It triangle RST and SUT,

`\angle RST=\angle SUT=90^(\circ)` (Definition of altitude)

`\angle STR=\angle UTS` (Common angle)

Two corresponding angles are equal. So by AA property of similarity,

`\triangle RST\sim \triangle SUT` .... (1)

It triangle RST and RUS,

`\angle RST=\angle SUR=90^(\circ)` (Definition of altitude)

`\angle SRT=\angle URS` (Common angle)

Two corresponding angles are equal. So by AA property of similarity,

`\triangle RST\sim \triangle RUS` .... (2)

According to transitive property of equality,

if a=b and b=c, then a=c.

From (1) and (2), we get

`\triangle RUS\sim \triangle SUT` ( Transitive property of equality)

Therefore the correct option is 1.