Answered

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

Prove: △AOK ≅ △BOL

Sagot :

MrRoyal

There are several ways two triangles can be congruent.

[tex]\mathbf{\triangle AOK \cong \triangle BOL}[/tex] are congruent by SAS

In [tex]\mathbf{\triangle AOL}[/tex] and [tex]\mathbf{\triangle BOK}[/tex] (see attachment), we have the following observations

[tex]1.\ \mathbf{AO = BO}[/tex] --- Because O is the midpoint of line segment AB

[tex]2.\ \mathbf{\angle AOL = BOK}[/tex] ---- Because vertical angles are congruent

[tex]3.\ \mathbf{LO = KO}[/tex] --- Because O is the midpoint of line segment KL

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

[tex]\mathbf{\triangle AOK \cong \triangle BOL}[/tex] ---- 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:

https://brainly.com/question/20517835

View image MrRoyal
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