Answer:
ΔAOK ≅ ΔBOL by SAS
Step-by-step explanation:
Hello there!
We are given:
Line segment AB intersects line segment KL at point O
O is the midpoint of AB
O is the midpoint of L
We want to prove that ΔAOK is congruent to ΔBOL
From the given picture, line segments AK and LB don't exist, but we can draw them in
Once we've drawn them in, we can use the given information to help us
Since O is the midpoint of AB, AO = OB by the definition of a midpoint
O is also the midpoint of LK, and because of that, LO=OK, also because of the definition of a midpoint
Since O is the intersection of AB and KL, that means that O would help form the vertical angles <LOB and <KOA (which are congruent because of vertical angles theorem)
Now, we have 2 sides and an angle which are congruent.
In the answer, we already have ΔAOK filled in
Remember that when naming congruent triangles, the congruent pieces need to match
A corresponds with B
O corresponds with O
K corresponds with L
So, that means ΔAOK ≅ ΔBOL
The reason is because of SAS (side-angle-side). The reason why it's SAS is because we have 2 pairs of congruent sides and one angle which is congruent
Please see the picture below if you'd like a visual aid
Hope this helps!
