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If Two Sides of a Triangle Are Unequal, Then the Angle Opposite to the Greater Side Is Greater Than Angle Opposite to the Smaller Side

In the adjoin...

Question

In the adjoining figure, PQ $=$ PR and QL $=$ MR. Prove that PL $=$ PM.

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Solution

In $△ P Q L$ and $△ P R M$
$P Q = P R$ [ Given ]
$∠ P Q L = ∠ P R M$ [ angles opposite to equal sides are also equal ]
$Q L = M R$ [ Given ]
$∴$ $△ P Q L ≅ △ P R M$ [ By SAS congruence rule ]
$\Rightarrow$ $P L = P M$ [ CPCT ]

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Similar questions

△ P Q R, Q M

P R

P R^{2} - P Q^{2} = Q R^{2}

Q M^{2} = P M \times M R

△ P Q R, P R^{2} - P Q^{2} = Q R^{2}

M

P R

Q M ⊥ P R

Q M^{2} = P M \times M R

△ P Q R

L

M

Q R

∠ L P Q = ∠ Q R P

∠ R P M = ∠ R Q P

Q L \times R M = P L \times P M

Δ P Q R,

P R^{2} - P Q^{2} = Q R^{2}

Q M ⊥ P R

Q M^{2} = P M \times M R

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