State the congruency of following pairs of triangles.
In $Δ A B C$ and $Δ P Q R$ , $B C = Q R,$ $∠ A = 9 0^{\circ}, ∠ C = ∠ R = 4 0^{\circ}$ and $∠ Q = 5 0^{\circ}$ .

Question

State the congruency of following pairs of triangles.
In $Δ A B C$ and $Δ P Q R$ , $B C = Q R,$ $∠ A = 9 0^{\circ}, ∠ C = ∠ R = 4 0^{\circ}$ and $∠ Q = 5 0^{\circ}$ .

Answer 1

In $△ A B C$ ,
$∠ A = 9 0^{o}$ , $∠ C = 4 0^{o}$
Sum of all angles of a triangle $= 18 0^{o}$
$∠ A + ∠ B + ∠ C = 18 0^{o}$
$9 0^{o} + ∠ B + 4 0^{o} = 18 0^{o}$
$∴ ∠ B = 5 0^{\circ}$

Now, In $△ A B C$ and $△ P Q R$
$B C = Q R$ (Given)
$∠ C = ∠ R = 4 0^{o}$ (Given)
$∠ B = ∠ Q = 5 0^{o}$
Thus, $△ A B C ≅ △ P Q R$ (ASA rule)

Answer 2

In

△ A B C

,

∠ A = 9 0^{o}

,

∠ C = 4 0^{o}

Sum of all angles of a triangle

= 18 0^{o}

∠ A + ∠ B + ∠ C = 18 0^{o}

9 0^{o} + ∠ B + 4 0^{o} = 18 0^{o}

∴ ∠ B = 5 0^{\circ}

Now, In

△ A B C

and

△ P Q R

B C = Q R

(Given)

∠ C = ∠ R = 4 0^{o}

(Given)

∠ B = ∠ Q = 5 0^{o}

Thus,

△ A B C ≅ △ P Q R

(ASA rule)

State the congruency of following pairs of triangles.
In $Δ A B C$ and $Δ P Q R$ , $B C = Q R,$ $∠ A = 9 0^{\circ}, ∠ C = ∠ R = 4 0^{\circ}$ and $∠ Q = 5 0^{\circ}$ .

$A S A$

$S S S$

$S A S$

Not congruent

Answer

Practice important Questions

Class 9 Maths Chapter 1 to 30

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SSS

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Answer

In △ABC, ∠A=90o, ∠C=40o Sum of all angles of a triangle =180o ∠A+∠B+∠C=180o 90o+∠B+40o=180o ∴∠B=50∘ Now, In △ABC and △PQR BC=QR (Given) ∠C=∠R=40o (Given) ∠B=∠Q=50o Thus, △ABC≅△PQR (ASA rule)

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Class 9 Maths Chapter 1 to 30

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