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Standard X

Mathematics

SAS Similarity

In the figure...

Question

In the figure given below, $A P = 2 P B$ and $C P = 2 P D$ .
(i) Prove that $△ A C P$ is similar to $△ B D P$ and $A C ∥ B D$ .
(ii) If $A C = 4.5 c m$ , calculate the length of $B D$ .

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Solution

From the question it is give that,
$A P = 2 P B, C P = 2 P D$
(i) We have to prove that, $△ A C P$ is similar to $△ B D P$ and $A C ∥ B D$
$A P = 2 P B$
$A P / P B = 2 / 1$
Then, $C P = 2 P D$
$C P / P D = 2 / 1$
$∠ A P C = ∠ B P D$ [from vertically opposite angles]
So, $△ A C P \sim △ B D P$
Therefore, $∠ C A P = ∠ P B D$ [alternate angles]
Hence, $A C ∥ B D$
(ii) $A P / P B = A C / B D = 2 / 1$
$A C = 2 B D$
$2 B D = 4.5 c m$
$B D = 4.5 / 2$
$B D = 2.25 c m$ .

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In the figure given below, AP=2PB and CP=2PD.(i) Prove that △ACP is similar to △BDP and AC∥BD.(ii) If AC=4.5 cm, calculate the length of BD.

In the figure given below, $A P = 2 P B$ and $C P = 2 P D$ .
(i) Prove that $△ A C P$ is similar to $△ B D P$ and $A C ∥ B D$ .
(ii) If $A C = 4.5 c m$ , calculate the length of $B D$ .