☑️Is there Anyone Genius to answer both the Parts of this question????☑️
Answer it Correctly!
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Step-by-step explanation:
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Given :
- AB = PQ
- BC = QR
- Median AM = Median PN
To Prove :
- △ABM ≅ △PQN
- △ABC ≅ △PQR
Solution :
1》△ABM ≅△PQN
In △ABM and △PQN
AB = PQ [ given ]
AM = PN [ given ]
BC = QR
half BC = half QR
BM = QN
Therefore, △ABM ≅△PQN [by SSS congruence]
∠ABM = ∠PQN [ by CPCT ]
2》△ABC ≅ △PQR
In △ABC and △PQR
AB = PQ [ given ]
BC = QR [ given ]
∠ABM = ∠PQN [ proved above ]
Therefore, △ABC ≅ △PQR [ by SAS congruence ]
Additionally :
Congruence rule:-
- SSS - If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
- SAS - If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.
- ASA - If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.
- AAS - If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.
- RHS - If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent.
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