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
[tex]\frac{PQ}{QR}=\frac{30}{15} = \frac{2}{1}[/tex] ..............( 1 )
[tex]\frac{QT}{RS}=\frac{28}{14} = \frac{2}{1}[/tex] ..............( 2 )
[tex]\frac{TP}{SQ}=\frac{20}{10} = \frac{2}{1}[/tex] ..............( 3 )
So By equation ( 1 ), ( 2 ) and ( 3 ) we get
[tex]\frac{PQ}{QR}=\frac{QT}{RS} = \frac{TP}{SQ}[/tex]
Now in Δ PQT and Δ QRS we have
[tex]\frac{PQ}{QR}=\frac{QT}{RS} = \frac{TP}{SQ}[/tex]
Which are corresponding sides of a similar triangle in proportion.
∴ Δ PQT ~ Δ QRS .....{S-S-S test for similarity}...Proved
