Question

Segments

Answer 1

There are several ways two triangles can be congruent.

• $\mathbf{AC = BD}$ congruent by SAS
• $\mathbf{\angle ABC \cong \angle BAD}$ congruent by corresponding theorem

In $\mathbf{\triangle AOL}$ and $\mathbf{\triangle BOK}$ (see attachment), we have the following observations

$1.\ \mathbf{AO = DO}$ --- Because O is the midpoint of line segment AD

$2.\ \mathbf{BO = CO}$ --- Because O is the midpoint of line segment BC

$3.\ \mathbf{\angle AOB =\angle COD}$ ---- Because vertical angles are congruent

$4.\ \mathbf{\angle AOC =\angle BOD}$ ---- Because vertical angles are congruent

Using the SAS (side-angle-side) postulate, we have:

$\mathbf{AC = BD}$

Using corresponding theorem,

$\mathbf{\angle ABC \cong \angle BAD}$ ---- i.e. both triangles are congruent

The above congruence equation is true because:

1. 2 sides of both triangles are congruent
2. 1 angle each of both triangles is equal
3. Corresponding angles are equal

See attachment

Read more about congruence triangles at:

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