Question

Отрезки AK и BM пересекаются в точке О и делятся пополам Докажите что AOB равно KOM

Answer 1

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Answer 2

Given Information

We are given that the line segments AK and BM intersect at point O and divide each other in half. We need to prove that triangle AOB is congruent to triangle KOM.

Proof

To prove that triangle AOB is congruent to triangle KOM, we can use the Side-Angle-Side (SAS) congruence criterion.

1. Side AO = Side KO: Since the line segments AK and BM divide each other in half, it means that AO is equal to KO. This is because both AO and KO are half of the line segment AK. Therefore, Side AO is equal to Side KO.

2. Side OB = Side OM: Similarly, since the line segments AK and BM divide each other in half, it means that OB is equal to OM. This is because both OB and OM are half of the line segment BM. Therefore, Side OB is equal to Side OM.

3. Angle AOB = Angle KOM: The line segments AK and BM intersect at point O, which means that angle AOB and angle KOM are vertical angles. Vertical angles are always congruent. Therefore, Angle AOB is equal to Angle KOM.

Based on the SAS congruence criterion, we have shown that Side AO = Side KO, Side OB = Side OM, and Angle AOB = Angle KOM. Therefore, triangle AOB is congruent to triangle KOM.

Conclusion

We have proved that triangle AOB is congruent to triangle KOM using the SAS congruence criterion.