`Delta\ A B C\ a n d\ Delta\ A B D` are on a common base `A B ,\ a n d\ A C\ =\ B D\ a n d\ B C\ =\ A D` as shown in Fig. 18. Which of the following statements is true? `DeltaA B C~=DeltaA B D` `DeltaA B C~=DeltaA D B` `DeltaA B C~=DeltaB A D`

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

If a, b, c, d are in proportion, then a : b = c : d and written as a : b : : c : d . Which of the following is true?

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

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 Fig. 7.21, A C\ =\ A E , A B\ =\ A D and /_B A D\ =/_E A C . Show that B C\ =\ D E .

In square A B C D ,\ P\ a n d\ Q are mid-point of A B\ a n d\ C D respectively. If A B=8c m\ a n d\ P Q\ a n d\ B D intersect at O , then find area of O P B

A B C\ a n d\ D B C are two isosceles triangles on the same bas B C and vertices A\ a n d\ D are on the same side of B C . If A D is extended to intersect B C at P , show that A B D\ ~= A C D (ii) A B P\ ~= A C P

In a parallelogram A B C D diagonals A C\ a n d\ B D intersect at O\ a n d\ A C=6. 8\ c m\ a n d\ B D=5. 6 c m . Find the measures of O C\ a n d\ O D .

A B\ a n d\ C D are two chords of a circle such that A B=6\ c m ,\ C D=12\ c m\ a n d\ A B C Ddot If the distance between A B\ a n d\ C D is 3\ c m , find the radius of the circle.