Prove the following statement when two Triangles are similar the ratio of areas of those Triangles is equal to the ratio of squares of their corresponding sides
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Step-by-step explanation:
Step 1:
Given Data: Δ ABC ~ Δ PQR
To Prove: (ΔABC) / (ΔPQR) =
Step 2:
Draw AM ⊥ BC, PN ⊥ QR
(ΔABC) / (ΔPQR) = (½ × BC × AM) / (½ × QR × PN)
= BC/QR × AM/PN........................................... [I]
In Δ ABM and Δ PQN,
Step 3:
∠B = ∠Q (Δ ABC ~ Δ PQR)
∠M = ∠N (each 90°)
Step 4:
So, Δ ABM ~ Δ PQN
AM/PN = AB/PQ ... ………………. [ii]
AB/PQ = BC/QR = CA/RP (Δ ABC ~ Δ PQR)..................... [iii]
Step 5:
Therefore Equation (i)
(ΔABC) / (ΔPQR) = BC/QR × AM/PN
= AB/PQ × AB/PQ [From Equation (ii) and Equation (iii)]
Step 6:
Using Equation (iii)
(ABC) / (PQR) =>
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this is answer
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