If ^@AB ^@ and ^@ CD ^@ are perpendicular to ^@ BC ^@ and ^@ AB = CD^@, show that ^@ EB = EC.^@
    A B C E D


  1. Home
  2. Math
  3. All Questions
Answer:


Step by Step Explanation:
  1. We are given that ^@ \angle ABE = \angle DCE = 90^ \circ ^@ and ^@ AB = CD^@.

    We need to find the value of ^@ EB ^@.
  2. 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}@^
  3. As corresponding parts of congruent triangles are equal, we have ^@ \bf {EB = EC} ^@.

You can reuse this answer
Creative Commons License