Answer:
The Proof for 20.and 21 are below.
Step-by-step explanation:
20.
Given:
∠PTR ≅ ∠RSP
[tex]\overline{PT} \cong \overline{RS}[/tex]
To Prove:
ΔPQT ≅ ΔRQS
Proof:
In ΔPQT and ΔRQS
Statement Reason
1. ∠PTR ≅ ∠RSP 1. Given
2.∠PQT ≅ ∠RQS 2.Vertical Opposite Angle Theorem
3. [tex]\overline{PT} \cong \overline{RS}[/tex] 3. Given
4. ΔPQT ≅ ΔRQS 4.By Angle-Angle-Side Congruence test..Proved
21.
Given:
[tex]\overline{PO} \cong \overline{SO}[/tex]
O is the Mid point of NT
∴ NO ≅ TO
To Prove:
∠N ≅ ∠T
Proof:
In ΔPON and ΔSOT
Statement Reason
1. [tex]\overline{PO} \cong \overline{SO}[/tex] 1. Given
2.∠PON ≅ ∠SOT 2.Vertical Opposite Angle Theorem
3. [tex]\overline{NO} \cong \overline{TO}[/tex] 3. O is the Mid point of NT.
4. ΔPON ≅ ΔSOT 4.By Side-Angle-Side Congruence test.
5. ∠N ≅ ∠T 5. Corresponding Parts of Congruent Triangles are Congruent....Proved
