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In the diagram below Q lies on side NO and P lies on side OM such that angle QPO is congruent to angle MNO Prove QPxMO=QOMN

User ILuvLogix
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Answer:

QPxMO is equal to QOMN

Explanation:

Since we are given that angle QPO is congruent to angle MNO, we can conclude that triangle QPO is similar to triangle MNO.

Therefore, we can write:

QP / MN = PO / NO (corresponding sides of similar triangles)

Multiplying both sides by MN, we get:

QP = (PO / NO) * MN

Now, we can use this expression for QP to prove that QPxMO=QOMN:

QPxMO = QP + PO (by segment addition postulate)

QPxMO = [(PO / NO) * MN] + PO (substituting QP with (PO / NO) * MN)

QPxMO = PO * [(MN + NO) / NO] (factoring out PO)

QPxMO = PO * (MO / NO) (since MN + NO = MO)

Now, we can see that PO * (MO / NO) is the same as QOMN, which means:

QPxMO = QOMN

Therefore, we have proven that QPxMO is equal to QOMN.

Hope this helped, I'm sorry if it is wrong. If you need more help, ask me!
:]

User Darkwonder
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