Question

Please help?!

Determine if the triangles, ΔPQT and ΔQRS, are similar. If so, identify the similarity criterion.

Answer 1

sss similarity

Explanation:

i took the test

Answer 2

Δ PQT ~ Δ QRS .....{S-S-S test for similarity}...Proof is below.

Explanation:

Given:

In Δ PQT

PQ = 30 ft

QT = 28 ft

TP = 20 ft

In Δ QRS

QR = 15 ft

RS = 14 ft

SQ = 10 ft

To Prove:

Δ PQT ~ Δ QRS

Proof:

First we consider the ratio of the sides

`(PQ)/(QR)=(30)/(15) = (2)/(1)` ..............( 1 )

`(QT)/(RS)=(28)/(14) = (2)/(1)` ..............( 2 )

`(TP)/(SQ)=(20)/(10) = (2)/(1)` ..............( 3 )

So By equation ( 1 ), ( 2 ) and ( 3 ) we get

`(PQ)/(QR)=(QT)/(RS) = (TP)/(SQ)`

Now in Δ PQT and Δ QRS we have

`(PQ)/(QR)=(QT)/(RS) = (TP)/(SQ)`

Which are corresponding sides of a similar triangle in proportion.

∴ Δ PQT ~ Δ QRS .....{S-S-S test for similarity}...Proved