Question

If abcd is a trapezium in which ab is parallel to cd and ad then​

Answer 1

Answer:

Please complete the Question.......

.....

Answer 2

Answer:

Quadrilateral:

The closed figure formed by joining four non col-linear points in an order is called a quadrilateral.

Trapezium:

A quadrilateral in which one pair of opposite sides are parallel is called a trapezium.

Given,

ABCD is a trapezium in which AB||CD & AD=BC

To Show:

(i) ∠A = ∠B

(ii) ∠C = ∠D

(iii) ΔABC ≅ ΔBAD

(iv) diagonal AC = diagonal BD  

Construction: Draw a line through C parallel to DA intersecting AB produced at E.

Proof:

i)  

AB||CD(given)

AD||EC (by construction)

So ,ADCE is a parallelogram

CE = AD (Opposite sides of a parallelogram)

AD = BC (Given)

We know that ,

∠A+∠E= 180°

[interior angles on the same side of the transversal AE]

∠E= 180° - ∠A

Also, BC = CE

∠E = ∠CBE= 180° -∠A

∠ABC= 180° - ∠CBE

[ABE  is a straight line]

∠ABC= 180° - (180°-∠A)

∠ABC= 180° - 180°+∠A

∠B= ∠A………(i)

 (ii) ∠A + ∠D = ∠B + ∠C = 180°

 (Angles on the same side of transversal)

∠A + ∠D = ∠A + ∠C

 (∠A = ∠B) from eq (i)

 ∠D = ∠C

(iii) In ΔABC and ΔBAD,

AB = AB (Common)

∠DBA = ∠CBA(from eq (i)

AD = BC (Given)

ΔABC ≅ ΔBAD

 (by SAS congruence rule)

(iv)  Diagonal AC = diagonal BD

 (by CPCT as ΔABC ≅ ΔBAD)

Hope this will help you.