Question

In the given figure, ABCD is a quadrilateral in which AB || CD and AD || BC.Prove that angle ADC = angle ABC​

Answer 1

Therefore using the SSS property, ∠ADC = ∠ABC is proved.

Given:

ABCD is a quadrilateral in which CD is parallel to AB and BC is parallel to AD.

To Find:

To prove that ∠ADC = ∠ABC

Solution:

The given question can be solved as shown below.

Given that,

AB || CD and AD || BC.

Join AC to draw a diagonal

In ∆ABC and ∆ADC

⇒ AD = BC (opposite side)

⇒ AB = CD (opposite side)

⇒ AC=AC ( common side)

⇒ ∆ABC congruence ∆ADC ( S.S.S property)

Hence ∠ADC = ∠ABC

Therefore using the SSS property, ∠ADC = ∠ABC is proved.

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Answer 2

Step-by-step explanation:

all explanation has been written in photograph