PQR and SQR are two right triangles with common hypotenuse QR if PR and SQ intersect at M such that PM=3cm,MR=6cm,SM=4cm,find the length of MQ
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Prove that ΔPQM is similar to ΔSRM
∠QPM = ∠MSR (Both are 90º)
∠ PMQ = ∠ SMR (vertically opposite angles)
By AA property, ΔPQM is similar to ΔSRM
Using the property of similar figures:
PM/SM = MQ/MR
3/4 = MQ/6
4MQ = 3 x 6
4MQ = 18
MQ = 18 ÷ 4 = 4.5 cm
Answer: MQ = 4.5 cm
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