Question

15. In the given figure, PQ || RS and PQ = RS. Prove that APUQ =ASUR.​

Answer 1

Step-by-step explanation:

Given:-

In the given figure, PQ || RS and PQ = RS.

To prove :-

APUQ =ASUR.

Solution:-

From the given figure ,

PQ || RS

angle PUQ=angle RUS-------(1)

(Vertically opposite angles)

PQ|| RS and PS is a transversal then

angle QPU=angle RSU-------(2)

(alternative interior angles)

PQ || RS and QR is a transversal then

angle PQU=angle SRU-------(3)

(alternative Interior angle)

from(1),(2)&(3)

By AAA Property

∆PUQ~∆SUR

and given that, PQ=RS------(4)

from above equations we conclude that

APUQ =ASUR.

Hence, Proved.

Used concept:-

Two Parallel lines are interested by a transversal then

• alternative Interior angles are equal.
• Corresponding Angles are equal.
• Vertically opposite angles are equal.

Answer 2

answer is in attachment