Question

ABCD is a trapezium in which AB II CD and
AD = BC (see Fig. 8.23). Show that
(i) ZA= ZB
(ii) ZC= ZD
(iii) A ABCEA BAD
D
(iv) diagonal AC = diagonal BD​

Answer 1

Answer:

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Answer 2

(I) Since, AE// DC and CE// DA

Therefore AECD is a parallogram.

→ AD = CE

→ But AD = BC [ given]

CE = BC

<CBR = <E

Since , ABE is a straight line,

<ABC + <CBE = 180°

→ <ABC + <E = 180° —1

Since, AD//EC and AE is transversal

<ABC + <E = 180⁰. —2 [cointerior angles]

<ABC + <E = <A + <E [From 1 and 2]

<ABC = <A ie. <B = <A

hence Proved .

(ii) AB is parallel to DC

→ <A + <D = 180° and <B + <C = 180⁰ [Co-interior]

→ <A + <D = <B + <C

→ <D = <C [ As, <A = <B]

Hence Proved

(iii) In triangle ABC and Triangle BAD

1. AB = AB [COMMON]

2. AD = BC [ITS GIVEN]

3. <BAD = <ABC

Therefore ABC ≈ BAD [ By S.A.S.]

Hence Proved

(iv) Since, Triangle ABC ≈ Triangle BAD

→ AC = BD

ie. diagonal AC = diagnal BD

Hence Proved