If -PQR and -XYZ are congruent under the correspondence QPR - XYZ- then i - R - ii QR - iii - P - iv QP - v - Q - vi RP -

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Standard IX

Mathematics

Types of Angles Based on Measurement

If △PQR and △...

Question

If $△ P Q R$ and $△ X Y Z$ are congruent under the correspondence $Q P R \leftrightarrow X Y Z$ , then (i) $∠ R =$ (ii) $Q R =$ (iii) $∠ P =$ (iv) $Q P =$ (v) $∠ Q =$ (vi) $R P =$

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Solution

Solve for congruent condition
It is given that $△ P Q R$ and $△ X Y Z$ are congruent and the correspondence is $Q P R \leftrightarrow X Y Z$
According to the given data, $△ Q P R ≅ △ X Y Z$
So the sides are congruent
$\Rightarrow Q P = X Y, P R = Y Z, Q R = X Z$
The angles are congruent
$\Rightarrow ∠ R = ∠ Z, ∠ P = ∠ Y, ∠ Q = ∠ X$
Hence
$∠ R = ∠ Z$
$Q R = X Z$
$∠ P = ∠ Y$
$Q P = X Y$
$∠ Q = ∠ X$
$R P = Z Y$

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Question 63

Fill in the blanks to make the statement true.

If $Δ P Q R$ and $Δ X Y Z$ are congruent under the correspondence $Q P R \leftrightarrow X Y Z$ , then
(i) $∠ R =$ ___ (ii) QR = ___
(iii) $∠ P =$ ___ (iv) QP = ___
(v) $∠ Q =$ ___ (v) RP = ___

Question 6
Angles Q and R of a $Δ$ PQR are $25^{\circ}$ and $65^{\circ}$ .
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(i) $P Q^{2} + Q R^{2} = R P^{2}$
(ii) $P Q^{2} + R P^{2} = Q R^{2}$
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Angles Q and R of a ΔPQR are 25° and 65°.

Write which of the following is true:

(i) PQ² + QR²= RP²

(ii) PQ² + RP²= QR²

(iii) RP² + QR²= PQ²

In the given figure, ABCD is a square and $∠ P Q R = 90^{\circ}$ . If PB = QC = DR, prove that (i) QB = RC, (ii) PQ = QR, (iii) $∠ Q P R = 45^{\circ}$

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If △PQR and △XYZ are congruent under the correspondence QPR↔XYZ, then (i) ∠R= (ii) QR= (iii) ∠P= (iv) QP= (v) ∠Q= (vi) RP=

If $△ P Q R$ and $△ X Y Z$ are congruent under the correspondence $Q P R \leftrightarrow X Y Z$ , then (i) $∠ R =$ (ii) $Q R =$ (iii) $∠ P =$ (iv) $Q P =$ (v) $∠ Q =$ (vi) $R P =$