What postulate or theroem prove these triangles are

Ответ:

hiji0206

27.01.2022

Mathematics

The explanation is below.

Step-by-step explanation:

Given

C is the midpoint of $\overline{AD}$ and also C is the midpoint of $\overline{EB}$

$\overline{AC} = \overline{DC}\\ and\\\overline{BC} = \overline{EC}$

To Prove:

$\angle A \cong \angle D$

Proof:

$In\ \triangle ACB\ and\ \triangle DCE\\\overline{AC} \cong \overline{DC}\ \textrm{ C is the midpoint of AD}\\\angle ACD \cong \angle DCE\ \textrm{vertically opposite angles}\\\overline{BC} \cong \overline{EC}\ \textrm{ C is the midpoint of BE}\\\therefore \triangle ACB \cong \triangle DCE\ \textrm{ By Side-Angle-Side test}\\\therefore \angle BAC \cong \angle EDC\ \textrm{corresponding parts(angles) of congruent triangles}\\\therefore \angle A \cong \angle D\ \textrm{ Proved}$

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What postulate or theroem prove these triangles are congruent?

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