In Figure altitudes AD and CE of DABC intersect each other at the point P. Show that:(i) `DeltaA E P~ DeltaC D P` (ii) `DeltaA B D ~DeltaC B E` (iii) `DeltaA E P~ DeltaA D B`(iv) `DeltaP D C ~DeltaB E C`

In Figure altitudes AD and CE of A B C intersect each other at the point P. Show that:(i) DeltaA E P~ DeltaC D P (ii) DeltaA B D ~DeltaC B E (iii) DeltaA E P~ DeltaA D B (iv) DeltaP D C ~DeltaB E C

In Figure, two chords AB and CD intersect each other at the point P. Prove that: (i) DeltaA P C~ DeltaD P B (ii) A P*P B=C P*D P

In Figure, two chords AB and CD intersect each other at the point P. Prove that: (i) DeltaA P C~ DeltaD P B (ii) A P*P B=C P*D P

In Figure two chords AB and CD of a circle intersect each other at the point P (when produced) outside the circle. Prove that (i) DeltaP A C~ DeltaP D B (ii) P A * P B = P C * P D

In figure, if DeltaA B E~=DeltaA C D , show that DeltaA D E~ DeltaA B C .

In figure, if DeltaA B E~=DeltaA C D , show that DeltaA D E~ DeltaA B C .

In parallelogram ABCD, two points P and Q are taken on diagonal BD such that D P = B Q . Show that: (i) DeltaA P D~= DeltaC Q B (ii) A P = C Q (iii) DeltaA Q B~= DeltaC P D (iv) A Q = C P (v) APCQ is a parallelogram.

In Figure, A B\ a n d\ C D are two chords of a circle, intersecting each other at P such that A P=C P . Show that A B=C D .

DeltaA B C and DeltaD B C are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see Fig. 7.39). If AD is extended to intersect BC at P, show that (i) \ DeltaA B D~=DeltaA C D (ii) DeltaA B P~=DeltaACP (iii) AP bisects ∠ A as well as ∠ D (iv) AP is the perpendicular bisector of BC

DeltaA B C and DeltaD B C are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see Fig. 7.39). If AD is extended to intersect BC at P, show that (i) \ DeltaA B D~=DeltaA C D (ii) DeltaA B P~=DeltaACP (iii) AP bisects ∠ A as well as ∠ D (iv) AP is the perpendicular bisector of BC