CBSE Class 10 Maths (Basic) 2024 · Paper 430/2/1 · Question 34(a)

Triangles 5 marks Medium

In the given figure, altitudes

C E

and

A D

△ A B C

intersect each other at the point

P

. Show that

Triangle ABC with altitudes CE and AD meeting at P

Answer

(i)

△ A E P \sim △ C D P

by AA, since

∠ A E P = ∠ C D P = 9 0^{\circ}

and

∠ A P E = ∠ C P D

(vertically opposite); (ii)

△ A B D \sim △ C B E

by AA, since

∠ A D B = ∠ C E B = 9 0^{\circ}

and

∠ B

is common; (iii)

△ A E P \sim △ A D B

by AA, since

∠ A E P = ∠ A D B = 9 0^{\circ}

and

∠ B A D

is common. Hence proved.

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