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(I) ∆ Xyz ≅ ∆ Xpz (Ii) Yz = Pz (Iii) ∠Yxz = ∠Pxz - Mathematics

Sum

(i) ∆ XYZ ≅ ∆ XPZ
(ii) YZ = PZ
(iii) ∠YXZ = ∠PXZ

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Solution

In right Δ XYZ and Δ XPZ,

Side XY = SIde XP .......(given)

Hypotenuse XZ = hypotenuse XZ .........(common)

(i) ∴ Δ XYZ ≅ Δ XPZ ...........(R.H.S. Axiom)

Hence (ii) YZ = PZ .............(c.p.c.t.)

and (iii) ∠YXZ = ∠PXZ ...........(c.p.c.t.)

Hence proved.

Concept: Extend Congruence to Simple Geometrical Shapes E.G. Triangles, Circles.
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APPEARS IN

Selina Concise Mathematics Class 7 ICSE
Chapter 19 Congruency: Congruent Triangles
Exercise 19 | Q 10
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