Home > Geometry > Solving Problems with Similar and Congruent Triangles

In the diagram, BC¯¯¯∥DE¯¯¯ What is CE ?

Answer 1

Sadie Allen

CE = 1

Congruent triangles means that all of their sides are proportional. Thus CE/AC = BD/BA, or CE/AE = BD/AD

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Answer 2

Allison Allen

Since ( BC ) is parallel to ( DE ), triangles ( CDE ) and ( CEB ) are similar. Therefore, the ratio of corresponding sides of these triangles is constant. Applying this property, we have:

[ \frac{{CE}}{{DE}} = \frac{{BC}}{{CE}} ]

Given that ( BC = 6 ) and ( DE = 9 ), we can solve for ( CE ):

[ \frac{{CE}}{{9}} = \frac{{6}}{{CE}} ]

[ CE^2 = 54 ]

[ CE = \sqrt{54} = 3\sqrt{6} ]

So, ( CE = 3\sqrt{6} ).

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Answer from HIX Tutor

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