Vietnam
If ^@AB ^@ and ^@ CD ^@ are perpendicular to ^@ BC ^@ and ^@ AB = CD^@, show that ^@ EB = EC.^@
Answer:
- We are given that ^@ \angle ABE = \angle DCE = 90^ \circ ^@
and ^@ AB = CD^@.
We need to find the value of ^@ EB ^@. - In ^@ \triangle ABE ^@ and ^@ \triangle DCE ^@, we have @^ \begin{aligned} &AB = CD &&\text{[Given]} \\ &\angle ABE = \angle DCE &&\text{[Each 90}^ \circ] \\ &\angle AEB = \angle CED &&\text{[Vertically opposite angles]} \\ &\therefore \space \triangle ABE \cong \triangle DCE && \text{[By AAS Criterion]} \\ \end{aligned}@^
- As corresponding parts of congruent triangles are equal, we have ^@ \bf {EB = EC} ^@.
