Question

I need help with figuring out the statements and reasons

Answer 1

Given

`\bar{AB}\mleft\Vert\bar{DC}\mright?`

and E is the midpoint of AC.

Therefore,

`\bar{AE}\cong\bar{EC}\text{ (Reason: E is the midpoint of AC)}`

Since
`\angle AEB\cong\angle DEC\text{ (Reason: Vertical angles are congruent)}`

Therefore,

`\triangle\text{AEB }\cong\triangle\text{DEC (Reason: It supports the AAS congruency rule)}`
`\angle AEB=90\degree\text{ (Reason: Intersecting transversals are perpendicular to each other)}`

Therefore,

`\triangle\text{AEB and }\Delta DEC\text{ are right angled triangles}`