Question

i. In figure 15a , if x=y and a=b, prove that l||n. ii. In figure 15b , show that AB||EF.​

Answer 1

Step-by-step explanation:

i. x and y are corresponding angles, and they are equal.

Therefore, m||n

a and b are corresponding angles, and they are equal.

Therefore, l||m

Since, l||m and m||n

l||m||n

Therefore, l||n

ii. Angle FEC and Angle ECD are consecutive interior angles, and their sum is 180°.

(148°+32°= 180°

Angle FEC+ Angle ECD= 180°)

Therefore, EF||CD

Angle ABC and Angle BCD(Angle BCE+Angle ECD) are vertically opposite angles, and they are equal.

(33°+32°=65°

Angle ABC = Angle BCD)

Therefore, AB||CD

Since, AB||CD and CD||EF

AB||CD||EF

Therefore, AB||EF

hope it helps!