Question

Given:
AB
∩
KL
= O,
O − midpoint of
AB
,
O − midpoint of
LK

Prove: △AOK ≅ △BOL

Answer 1

There are several ways two triangles can be congruent.

$\mathbf{\triangle AOK \cong \triangle BOL}$ are congruent by SAS

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

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

$2.\ \mathbf{\angle AOL = BOK}$ ---- Because vertical angles are congruent

$3.\ \mathbf{LO = KO}$ --- Because O is the midpoint of line segment KL

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

$\mathbf{\triangle AOK \cong \triangle BOL}$ ---- 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

Read more about congruence triangles at:

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