Question

10. In trapezium ABCP, AB|| DC, find ZC and ZD.
55°
TE
А
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Answer 1

Step-by-step explanation:

Given: ABCD is a trapezium where

AB || CD and AD = BC

To prove: LA = ZB

Construction: Extend AB and draw a line through parallel to DA intersecting AB produced at E

Proof:

AD || CE

& AE || DC

(From construction)

(As AB || DC, &

AB is extended)

In AECD, both pair of opposite sides are parallel, AECD is a parallelogram

AD = CE parallelogram are equal)

(Given)

(In A BCE, Angles opposite to equal sides are equal)

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AD = CE

But AD = BC = BC = CE So, ZEN = ZONE

For AD || CE

& AE is the transversal ZA + ZEN = 180 °

ZA = 180° - ZEN

From (2) & (3) LA = ZB Hence proved