Question

EASY BRAINLIEST PLEASE HELP!!

Answer 1

Answer:

see below

Step-by-step explanation:

Proposition:

Let the diagonals AC and BD of the Parallelogram ABCD intercept at E. It is required to prove AE=CE and DE=BE

Proof:

1)The lines AD and BC are parallel and AC their transversal therefore,

$\displaystyle \angle DAC = \angle ACB \\ \ \qquad [\text{ alternate angles theorem}]$

2)The lines AB and DC are parallel and BD their transversal therefore,

$\displaystyle \angle BD C= \angle ABD \\ \ \qquad [\text{ alternate angles theorem}]$

3)now in triangle ∆AEB and ∆CED

• $\displaystyle \angle EAD=\angle ECB$
• $\angle EDA=\angle EBC$
• $\displaystyle AD=BC$

therefore,

$\displaystyle \Delta AEB \cong \Delta CED$

hence,

• AE=CE
• DE=BE

Proven