In the figure above- straight lines AB and CD intersect at P- and AC - BD- Then - APC and - BPD are similar-If true enter 1 else 0-

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Standard X

Mathematics

AAA Similarity

In the figure...

Question

In the figure above, straight lines $A B$ and $C D$ intersect at $P$ , and $A C | | B D$ . Then $Δ A P C$ and $Δ B P D$ are similar.If true enter 1 else 0.

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Solution

In $△ A P C$ and $△ B P D$
$∠ A P C = ∠ B P D$ (Vertically opposite angles)
$∠ P A C = ∠ P B D$ (Alternate angles of parallel lines AC and BD)
$∠ P C A = ∠ P D B$ (Third angle)
Thus, $△ A P C \sim △ B P D$ (AAA rule)

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In the figure above, straight lines AB and CD intersect at P, and AC || BD. Then ΔAPC and ΔBPD are similar.If true enter 1 else 0.

In △APC and △BPD∠APC=∠BPD (Vertically opposite angles)∠PAC=∠PBD (Alternate angles of parallel lines AC and BD) ∠PCA=∠PDB (Third angle)Thus, △APC∼△BPD (AAA rule)

In the figure above, straight lines $A B$ and $C D$ intersect at $P$ , and $A C | | B D$ . Then $Δ A P C$ and $Δ B P D$ are similar.If true enter 1 else 0.

In $△ A P C$ and $△ B P D$
$∠ A P C = ∠ B P D$ (Vertically opposite angles)
$∠ P A C = ∠ P B D$ (Alternate angles of parallel lines AC and BD)
$∠ P C A = ∠ P D B$ (Third angle)
Thus, $△ A P C \sim △ B P D$ (AAA rule)