Rectangle mnop is shown below. aiden argues that mnq is congruent to poq. what triangle congruence criteria proves that mnq is congruent to poq? select all that apply

1. angle-angle-side
2.angle-side-angle
3.side-side-angle
4.hypotenuse-angle
5.hypotenuse-leg

Δ MNQ ≅ Δ POQ ( BY Angle Angle Side)

Step-by-step explanation:

Given:

m∠NQM = 40°

m∠NQO = 100°

MNOP is a Rectangle

So we can say that:

Property of rectangle:

All angles of rectangle are 90°

Opposite sides of Rectangle are equal and parallel to each other

MN ≅ PO (opposite side of rectangle)

∠NMQ ≅ ∠OPQ (Both angles are 90°)

Now By Straight Angle property

m∠NQM + m∠NQO + m∠OQP = 180° (angles of straight line)

Substituting the values we get;

40° + 100° + m∠OQP = 180°

140° + m∠OQP = 180°

m∠OQP = 180° - 140° = 40°

So m∠OQP = m∠NQM = 40°

m∠OQP ≅ m∠NQM (Equals angles are congruent to each other)

Hence In Δ MNQ and Δ POQ

m∠OQP ≅ m∠NQM

∠NMQ ≅ ∠OPQ (Both angles are 90°)

MN ≅ PO (opposite side of rectangle)

Δ MNQ ≅ Δ POQ ( BY Angle Angle Side)

Hence Proved...

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step-by-step explanation: