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show your work for both questions

The Proof for question no 20 and 21 are below.

Step-by-step explanation:

20.

Given:

∠PTR≅∠RSP

PT ≅ RS

To Prove:

ΔPQT ≅ ΔRQS

Proof:

In ΔPQT and ΔRQS

Statements                    Reasons

1. ∠PTR ≅ ∠RSP       1 .Given

2. ∠PQT ≅ ∠ROS     2. Vertical Opposite Angle Theorem.

3. PT ≅ RS                3. Given

4. ΔPQT ≅ ΔRQS     4. By A-A-S Congruence Postulate Proved

21.

Given:

PO ≅ SO

O is the Mid Point of NT

To Prove:

∠N ≅ ∠T

Proof:

In ΔPON and ΔSOT

Statements                    Reasons

1. PO ≅ S O              1 .Given

2. ∠PON ≅ ∠SOT    2. Vertical Opposite Angle Theorem.

3. NO ≅ TO              3. O is the Mid Point of NT

4. ΔPON ≅ ΔSOT    4. By S-A-S Congruence Postulate

5. ∠N ≅ ∠T               5. Corresponding Parts of Congruent Triangles are Congruent .( CPCTC )...Proved

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Step-by-step explanation: