Congruence tests

<p>In parallelogram \(ABCD\), \(E\), \(F\) are on diagonal \(AC\) such that&nbsp;\(AE = CF\). \(BEH\) and \(DFG\) are straight lines. Prove that</p>
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<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-paragraph">triangles \(BAE\) and \(DCF\) are congruent,</div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">triangles \(BAH\) and \(DCG\) are congruent, and</div></li><li data-list-item-id="item-iii" data-list-item-path="item-iii"><div class="list-item-paragraph">quadrilateral \(BGDH\) is a parallelogram.</div></li></ol>

In parallelogram \(ABCD\), \(E\), \(F\) are on diagonal \(AC\) such that \(AE = CF\). \(BEH\) and \(DFG\) are straight lines. Prove that

triangles \(BAE\) and \(DCF\) are congruent,

triangles \(BAH\) and \(DCG\) are congruent, and

quadrilateral \(BGDH\) is a parallelogram.

Proofs in Plane Geometry - Congruence

Proofs in Plane Geometry - Congruence

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Solution:

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