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prove sss congurence rule
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prove sss congurence rule Related: Facts That Matter,Triangles Mathem...
SSS congruence criterion:
Two triangles are congruent if the three sides of one triangle are equal to the corresponding three sides of the other triangle
Given: ΔPQR and ΔXYZ are such that PQ = XY, QR = YZ and PR = XZ.
To prove: ΔPQR ΔXYZ
Construction: Draw YW such that ∠ZYW = ∠PQR and WY = PQ. Join XW and WZ.
Proof: In ΔPQR and ΔWYZ
QR = YZ (Given)
∠PQR = ∠ZYW (Construction)
PQ = YW (Construction)
∴ΔPQR ΔWYZ (SAS congruence criterion)
⇒∠P =∠W and PR = WZ (CPCT)
PQ = XY and PQ = XW
∴ XY = YW
Similarly, XZ = WZ
In ΔXYW, XY = YW
⇒ ∠YWX = ∠YXW (In a triangle, equal sides have equal angles opposite to them)
Similarly, ∠ZWX = ∠ZXW
∴ ∠YWX + ∠ZWX = ∠YXW + ∠ZXW
⇒ ∠W = ∠X
Now, ∠W = ∠P
∴ ∠P = ∠X
In ΔPQR and ΔXYZ ,
PQ = XY
∠P = ∠X
PR = XZ
∴ ΔPQR ΔXYZ
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prove sss congurence rule Related: Facts That Matter,Triangles Mathematics for Class 10th for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about prove sss congurence rule Related: Facts That Matter,Triangles Mathematics for Class 10th covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for prove sss congurence rule Related: Facts That Matter,Triangles Mathematics for Class 10th.
prove sss congurence rule Related: Facts That Matter,Triangles Mathematics for Class 10th for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about prove sss congurence rule Related: Facts That Matter,Triangles Mathematics for Class 10th covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for prove sss congurence rule Related: Facts That Matter,Triangles Mathematics for Class 10th.
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