Question

In the figure, AB| |CD. ∠AEB and ∠CED are congruent __1__ .

∠AEC and ∠ __2__ are congruent by the Vertical Angles Theorem.


1.

A. By the linear pair theorem.

B. By the vertical angles theorem.

C. because they are corresponding angles for parallel lines cut by a transversal.


2.

A. AEB

B. BED

C. ECD

D. EBA

Answer 1

2. is B. BED. I don't know 1. but I do know that C is wrong for that question so it is either A or B.

Answer 2

1. B. By the vertical angles theorem.

2. ∠BED

Explanation:

We have that, AB || CD and the two lines in between them are intersecting each other.

Since, we know that,

Vertical Angles Theorem states that 'Two opposite angles of the intersecting lines are congruent'.

So, as the lines are intersecting, we get by 'Vertical Angles Theorem',

∠AEB ≅ ∠CED and ∠AEC ≅ ∠BED.