In the given figure- prove that- -4 MARKS-i - X Y Z - X P Zii YZ - PZiii - Y XZ - P XZ

Steps: 1 Mark Each Proof: 1 Mark (i) In Δ XYZ and Δ XPZ XY=XP [Given] ∠ XYZ = ∠ XPZ = 90^∘ [Given] XZ = XZ [Common] ⇒Δ XYZ ≅Δ XPZ [RHS congruency criteria] ...

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Byju's Answer

Standard VII

Mathematics

RHS Criteria for Congruency of Triangles

In the given ...

Question

In the given figure, prove that: [4 MARKS]

(i) $Δ X Y Z ≅ Δ X P Z$

(ii) YZ = PZ

(iii) $∠ Y X Z = ∠ P X Z$

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Solution

Steps: 1 Mark
Each Proof: 1 Mark

(i) In $Δ X Y Z$ and $Δ X P Z$

$X Y = X P$ [Given]

$∠ X Y Z = ∠ X P Z = 90^{\circ}$ [Given]

$X Z = X Z$ [Common]

$\Rightarrow Δ X Y Z ≅ Δ X P Z$ [RHS congruency criteria]

(ii) $Y Z = P Z$ [Corresponding parts of congruent triangles]

(iii) $∠ Y X Z = ∠ P X Z$ [Corresponding parts of congruent triangles]

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In the given figure, prove that: [4 MARKS] (i) ΔXYZ≅ΔXPZ (ii) YZ = PZ (iii) ∠YXZ=∠PXZ

Steps: 1 Mark Each Proof: 1 Mark (i) In ΔXYZ and ΔXPZ XY=XP [Given] ∠XYZ=∠XPZ=90∘ [Given] XZ=XZ [Common] ⇒ΔXYZ≅ΔXPZ [RHS congruency criteria] (ii) YZ=PZ [Corresponding parts of congruent triangles] (iii) ∠YXZ=∠PXZ [Corresponding parts of congruent triangles]

In the given figure, prove that: [4 MARKS]

(i) $Δ X Y Z ≅ Δ X P Z$

(ii) YZ = PZ

(iii) $∠ Y X Z = ∠ P X Z$