Question

Q3: In the diagram, ABCD is a square.
Points P, Q, R and Slie on AB, BC, CD and DA so that AP=BQ=CREDS
B
S
R
С
(a) Giving all your reasons, show that
(i) PQR IS A RIGHT ANGLE ​

Answer 1

Step-by-step explanation:

Correct option is

A

45

Given: ABCD is a square.

thus, AB=BC

AP=BQ (Given)

AB−AP=BC−BQ

PB=CQ (I)

Now, In △PBQ and △CQR,

∠PBQ=∠QCR (Each 90

∘

)

PB=CQ (From I)

BP=CR (Given)

thus, △PBQ≅△CQR (SAS rule)

or, PQ=QR (By cpct)

Now, In △PQR

PQ=QR

thus, ∠PRQ=∠QPR=x (Isosceles triangle property)

∠PQR=90

∘

(Given)

Sum of angles = 180

∠PQR+∠QPR+∠QRP=180

90+x+x=180

2x=90

x=45

Thus, ∠PRQ=45

∘

Answer 2

Answer:

PQR is a tight angle T

angle par = 45°