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Use the diagram below in the following given information to prove the opposite size of a parallelogram are congruent

Use the diagram below in the following given information to prove the opposite size of a parallelogram are congruent
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Use the diagram below in the following given information to prove the opposite size of a parallelogram are congruent

Use the diagram below in the following given information to prove the opposite size-example-1
User Lmop
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1 Answer

5 votes

Given:

ABCD is a parallelogram.

To prove:


AD\cong BC\text{ and AB}\cong CD

Proof:


\begin{gathered} \text{ABCD is a parallelogram}\ldots\ldots\text{ given.} \\ DC\parallel AB\text{ and AD}\parallel BC\ldots\ldots..by\text{ definition of parallelogram} \\ \angle\text{DCA congruent to }\angle\text{BAC; }\angle BCA\text{ congruent to }\angle DAC\ldots\ldots\text{.}AI\text{ angles theorem} \\ AC\cong AC\ldots.\text{ reflexive property} \\ \Delta ADC\cong\Delta CBA\ldots.by\text{ ASA} \\ AD\cong BC\text{ and AB}\cong CD\ldots\ldots by\text{ CPCTC} \end{gathered}

Hence proved.

Use the diagram below in the following given information to prove the opposite size-example-1
User Gandolf
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