Question

5.
SECTION B
Fro the figure 5 as shown If PQ || ST, AB is line
passing through the point S, ZQSA = 28°,find the
measure of ZTSB
989
fig 5

Question number 5 please....
Thanking in advance!

Answer 1

Answer:Given:

ST || QR

PT= 4 cm

TR = 4cm

In ΔPST and ΔPQR,

∠SPT = ∠QPR (Common)

∠PST = ∠PQR (Corresponding angles)

ΔPST ∼ ΔPQR (By AA similarity criterion)

We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.

ar(∆PST) /ar(∆PQR)= (PT)²/(PR)²

ar(∆PST) /ar(∆PQR)= 4²/(PT+TR)²

ar(∆PST) /ar(∆PQR)= 16/(4+4)²= 16/8²=16/64= 1/4

Thus, the ratio of the areas of ΔPST and ΔPQR is 1:4.

HOPE THIS WILL HELP YOU...

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Step-by-step explanation: