In `DeltaA B C`, AD is the perpendicular bisector of BC (see Fig. 7.30). Show that `DeltaA B C`is an isosceles triangle in which `A B\ =\ A C`.

In Delta ABC , AD is the perpendicular bisector of BC (see Fig. 7.30). Show that Delta ABC is an isosceles triangle in which A B\ =\ A C .

In DeltaABC , the bisector AD of angleA is perpendicular to side BC (see figure). Show that AB =AC or DeltaABC is isosceles.

AD and BC are equal perpendiculars to a line segment AB (see Fig. 7.18). Show that CD bisects AB.

In quadrilateral ACBD, A C\ =\ A D and AB bisects /_A (see Fig. 7.16). Show that DeltaA B C~=DeltaA B D

In a Delta ABC , the median AD is perpendicular to AC. If b = 5 and c = 11, then a =

In bigwedge ABC, the bisector AD of A is perpendicular to side BC( see Fig.7.27). Show that AB backslash=backslash AC and Delta ABC is isosceles

ABC and DBC are two isosceles triangles on the same base BC (see Fig. 7.33). Show that /_A B D\ =/_A C D

D is a point on side BC of Delta ABC such that AD=AC (see Fig.7.47). Show that AB>AD

ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig. 7.32). Show that (i) DeltaA B E~=DeltaA C F (ii) A B\ =\ A C , i.e., ABC is an isosceles triangle.

In DeltaA B C , D, E and F are respectively the mid-points of sides AB, BC and CA. Show that DeltaA B C is divided into four congruent triangles by joining D, E and F.