Question

given <BCA =<DCE
<B and < D are right angles
C is the midpoint of BD
prove BA=DE

Answer 1

Answer on Question #71257 – Math – Geometry

Question

Given $\angle BCA = \angle DCE$,

$\angle B$ and $\angle D$ are right angles,

$C$ is the midpoint of $BD$.

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Prove $BA = DE$

Solution

Given

$$\angle BCA = \angle DCE = \alpha$$

Consider triangles $\Delta BCA, \Delta DCE$ and apply the definition of the tangent

$$\tan \alpha = \frac{BA}{BC} = \frac{DE}{DC} \quad (1)$$

It is given that $C$ is a midpoint of $BD$, then

$$BC = DC \quad (2)$$

It follows from (1) and (2) that

$$BA = DE$$

QED.

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