`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 .

In two triangles A B C\ a n d\ A D C , if A B=A D\ a n d\ B C=C Ddot Are they congruent?

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 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 A B D C\ a n d\ A D B Cdot Prove that /_D A B=\ /_D C B

In Delta A B C ,\ if\ a=18 ,\ b=24\ a n d\ c=30\ a n d\ /_C=90^0 find sin A ,\ sin B\ a n d\ sin Cdot

In a DeltaA B C prove that cos(A+B)+cos C=0.

In Figure, A B C\ a n d\ D B C are two triangles on the same base B C such that A B=A C\ a n d\ D B=D Cdot Prove that /_A B D=/_A C D

In Figure, it is given that A B=C D\ a n d\ A D=B C. Prove that A D C\ ~= C B A .

In a DeltaA B C ,\ if\ b=sqrt(3),\ c=1\ a n d\ /_A=30^0 , then find a