Question

ABCD is a trapezium in which AB//CD if AD=BC show that ZA ZC=ZD

Answer 1

Answer:

lo sure you too I hope you have a great day k Liye to get a new one side

Answer 2

Answer:

Given ABCD is trapezium where AD=BC.

(i) To prove: ∠A=∠B

we can see that AECD is a parallelogram, so sum of adjacent angles =180

→∠A+∠E=180

→∠A+x=180

→∠A=180 −x=∠B

Hence proved.

(ii) To prove: ∠C=∠D

sum of adjacent angles in parallelogram is π, so

→∠D∠C+180

−2x=180

→∠C+∠D=2x

Now

→∠B+∠C=180

→180 −x+∠C=180

=0 ∠C=x

∠D=x

And,

∠C=∠D

Hence proved.

(iii) ΔABC=ΔBAD

→ side AB is common.

→AD=BC (given)

so the angle including both the sides is also same,

∠A=∠B. So

ΔABC=ΔBAD (By SAS congruent Rule)

Hence proved.

(iv) As ΔABC=ΔBAD

The third side of both triangles i.e. diagonals are equal AC=BD