`DeltaABC and DeltaDBC` are two isosceles triangles on thesame base BC (see figure). Show that `/_ ABD = /_ ACD.`

In the adjacent figure DeltaABC and DeltaDBC are two triangles such that bar(AB) = bar(BD) and bar(AC) = bar(CD) . Show that DeltaABC ~= DeltaDBC.

DeltaABC is an isosceles triangle in which AB = AC. Show that /_ B = /_ C.

DeltaABC and DeltaDBC are situated on the same base BC and on the same side of BC . E is any point on the side BC . Two line through the point E and parallel to AB and BD intersects the sides AC and DC at the points F and G respectively. Prove that AD||FG .

D is a point on side BC ΔABC such that AD = AC (see figure). Show that AB > AD.

In the figure, ΔABC and ΔABD are two triangles on the same base AB. If line segment CD is bisected by bar(AB) at O, show that ar (DeltaABC) = ar (DeltaABD).

DeltaABC and DeltaBDE are two equilateral triangles. If D is the mid-point of BC , then the ratio of the areas of DeltaABC and DeltaBDE is

E and F are respectively the mid-points of equal sides AB and AC of DeltaABC (see figure) Show that BF = CE.

DeltaABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see figure). Show that /_BCD is a right angle.

In an isosceles triangle ABC with AB = AC, D and E are points on BC such that BE = CD. Show that AD = AE.

If ABC is an isosceles triangle and D is a point on BC such that AD bot BC , then____