`triangle` ABC and `triangle` DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see the given figure). If AD is extended to intersect BC at P, show that, ( i ) `triangle ABD = triangle ACD (ii) triangle ABP = triangle ACP` (iii) AP bisects `angle` A as well as `angle` D. (iv) AP is the perpendicular bisector of BC

triangle ABC and triangle DBC are isosceles triangles on the same base BC. Prove that line AD bisects BC at right angles

ABC and DBC are two isosceles triangles on the same base BC (see the given figure). Show that angle ABD = angle ACD .

In triangle ABC, AB = AC and the bisector of angle A lt intersects BC at D. Prove that, ( 1 ) triangle ADB = triangle ADC ( 2 ) angle ABC = angle ACB

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

ABCD is a quadrilateral in which AD = BC and angle DAB = angle CBA (see the given figure). Prove that ( i ) triangle ABD = triangle BAC, ( ii) BD = AC and (iii) angle ABD = angle BAC

In the given figure, ABC and DBC are two triangles on the same base BC. Prove that (ar(ABC))/(ar(DBC))= (AO)/(DO) .

ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that ( i ) triangle ABE ~= triangle ACF (ii) AB = AC i.e ABC is an isoceles triangle

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