What is the midpoint of a segment whose endpoints are (–4, –2) and (5, 1)?
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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
..............( 1 )
..............( 2 )
..............( 3 )
So By equation ( 1 ), ( 2 ) and ( 3 ) we get
Now in Δ PQT and Δ QRS we have
Which are corresponding sides of a similar triangle in proportion.
∴ Δ PQT ~ Δ QRS .....{S-S-S test for similarity}...Proved