Question

Please help?!

Answer 1

Answer:

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

Step-by-step 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

$\frac{PQ}{QR}=\frac{30}{15} = \frac{2}{1}$            ..............( 1 )

$\frac{QT}{RS}=\frac{28}{14} = \frac{2}{1}$            ..............( 2 )

$\frac{TP}{SQ}=\frac{20}{10} = \frac{2}{1}$            ..............( 3 )

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

$\frac{PQ}{QR}=\frac{QT}{RS} = \frac{TP}{SQ}$

Now in Δ PQT  and Δ QRS we have

$\frac{PQ}{QR}=\frac{QT}{RS} = \frac{TP}{SQ}$

Which are corresponding sides of a similar triangle in proportion.

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