Question

Please quick and real answers!

Give the reason for each statement in the proof. Statements may be used more than once and not all statements will be used.

GIVEN: QM¯¯¯¯¯¯¯¯¯ ∥ OP¯¯¯¯¯¯¯¯
PROVE: △QNM ∼ △ONP


STATEMENTS REASONS
1. QM¯¯¯¯¯¯¯¯¯ ∥ OP¯¯¯¯¯¯¯¯ 1. Response area
2. ∠MQN ≅ ∠PON 2. Response area
3. ∠MNQ ≅ ∠PNO 3. Response area
4. △QNM ∼ △ONP 4. Response area

Answer 1

Reason 1: Given

It is already given that QM ║ OP

Reason 2: Alternate interior angles

Since ∠MQN and ∠PON are alternate interior angles, they are congruent.

Reason 3: Vertical angles

∠MNQ and ∠PNO are vertically opposite angles and hence, due to that, equal.

Reason 4: AA postulate

2 Angles of the triangle are congruent. which makes the triangle congruent by AA (Angle-Angle) Postulate.

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