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Equal Angles Subtend Equal Sides

In adjoining ...

Question

In adjoining figure, LN=6 cm, PM=3 cm and PN=6 cm, LM=3 cm
(a)Is $△ L M N = △ P M N$
(b)If yes, state the three pairs of equal parts.
(c)Is $∠ L = ∠ P$ , Why?

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Solution

Consider $Δ L M N$ and $Δ P M N$
$L M = P M = 3 c m L N = N P = 6 c m N M = N M ⟹ Δ L M N = Δ P M N$
$∠ L = ∠ P$ since they are corresponding angles

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$△ L M N \sim$ $△ X Y Z$ . In $△ L M N, L M = 6 c m, M N = 6.8 c m, L N = 7.6 c m$ and $\frac{L M}{X Y} = \frac{4}{5}$ ; Construct $△ X Y Z$ .

△

~

△

△

\frac{LM}{XY} = \frac{4}{3}

△

∆

∠

°

-

L M N

∠ L = 120^{\circ}

L M = 4

L N = 5

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