Question

pls do this sum fast its urgent??​

Answer 1

Given :

• side PQ = side QR
• side PR = side RD

To prove :

• ∠ QPD : ∠ PDQ = 3:1

Proof :

In ∆ PQR,side PQ = QR, so using the isosceles triangle theorem,we know that :

∠ QPR = ∠ QRP = x -----> (1)

Similarly,it is given that side PR = side RD,so using the isoceles triangle theorem,

∠ RPD = ∠ PDQ = y ----> (2)

From figure,it can be seen that :

∠ QPD = ∠ QPR + ∠ RPD

∠ QPD = x + y ----> (3)

Now, using exterior angle theorem,we can say that :

∠ PRQ = ∠ RPD + ∠ PDQ

x = y + y

x = 2y -----> (4)

Now substitute value of x from equation (4) in equation (3),

∠QPD = 2y + y

∠ QPD = 3y -----> (5)

From (2) we know that ∠ PDQ = y

So,now divide equation (5) by equation (2),

→ (∠QPD)/(∠PDQ)

→ 3y/y

→ 3/1

Hence proved → ∠QPD: ∠PDQ = 3:1.

You can probably send me some chocolates for helping you out, I'll be waiting in my dream xD