In the diagram, $\Delta ABC\equiv \Delta CED$, $AB=10$ cm, $DC=25$ cm, \(\angle BAC=90{}^\circ

Question

In the diagram, $\Delta ABC\equiv \Delta CED$, $AB=10$ cm, $DC=25$ cm, $\angle BAC=90{}^\circ $ and $\angle ABC=60{}^\circ $. Find the length of $CE$, the area of $\Delta CED$, $\angle CDE$, $\angle BFE$. Source check: the stated congruence makes the perpendicular legs of triangle $ABC$ equal to $10$ cm and $25$ cm. These imply $\angle ABC=\tan^{-1}(25/10)\approx68.2^\circ$, not the printed $60^\circ$. Thus the complete set of givens is inconsistent. The length/area results below use the given sides and congruence; the angle results are conditional on the printed angles.

Accepted Answer

$\text{(a)}\ 10\text{ cm}$ $\text{(b)}\ 125\text{ cm}^2$ $\text{(c)}\ 30^\circ$ $\text{(d)}\ 90^\circ$ Results are conditional as explained in the source check; the complete printed givens are inconsistent.

Congruent Right Triangles: Lengths, Areas and Angles

Congruent Right Triangles: Lengths, Areas and Angles

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