Question

ABCDis a trapezium in which AB||CD and AD=BC.show that.a)LA=LB.b)LC=LD.c)​

Answer 1

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 =180o

→∠A+∠E=180o

→∠A+x=180o

→∠A=180o−x=∠B

Hence proved.

(ii) To prove: ∠C=∠D

sum of adjacent angles in parallelogram is π, so 

→∠D∠C+180o−2x=180o

→∠C+∠D=2x

Now

→∠B+∠C=180o

→180o−x+∠C=180o=0        ∠C=x, so  

                                                          ∠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

Answer 2

Answer:

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