Mathematics
In the figure (1) 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.
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Answer
(i) Given, AP = 2PB and CP = 2PD.
∠ APC = ∠ BPD [Vertically opposite angles]
So by SAS rule of similarity △ACP ~ △BDP.
Since, triangles are similar,
∴ ∠ CAP = ∠ PBD.
Since, these angles are alternate angles therefore, AC ∥ BD.
Hence, proved that △ACP ~ △BDP and AC ∥ BD.
(ii) Since triangles are similar. So,
Hence, BD = 2.25 cm.
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