If `DeltaA B C` is an isosceles triangle such that `A B=A C ,\ ` then altitude `A D` from `A` on `B C` bisects `B C` (Fig.43).

If A B C is an isosceles triangle such that A B=A C and A D is an altitude from A on B C . Prove that (i) /_B=/_C (ii) A D bisects B C (iii) A D bisects /_A

If the altitude from one vertex of a triangle bisects the opposite side, then the triangle is isosceles. GIVEN : A A B C such that the altitude A D from A on the opposite side B C bisects B C i.e., B D=D Cdot TO PROVE : A B=A C i.e. the triangle A B C is isosceles.

Delta ABC is an isosceles triangle in which A B= A C . Side BA is produced to D such that A D = A B (see Fig. 7.34). Show that /_B C D is a right angle.

ABC is an isosceles triangle inscribed in a circle of radius rdot If A B=A C and h is the altitude from A to B C , then triangle A B C has perimeter P=2(sqrt(2h r-h^2)+sqrt(2h r)) and area A= ____________ and = __________ and also ("lim")_(xvec0)A/(P^3)=______

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

A B C is an isosceles triangle such that A B=A C a n d A D is the median to base B C . Then, /_B A D= 55^0 (b) 70^0 (c) 35^0 (d) 110^0

DeltaA B C is isosceles with A B=A Cdot A D is the altitude from A on B Cdot Is DeltaA B D~=DeltaA C D ? State the pairs of matching parts you have used to answer (i). Is it true to say that B D= D C ?

In an isosceles triangle A B C , if A B=A C=25 c m and B C=14 c m , then the measure of altitude from A on B C is (a) 20cm (b) 22cm (c) 18cm (d) 24cm

A triangle A B C is an isosceles triangle if any one of the following conditions hold: Altitude A D bisects /_B A Cdot Bisector of /_B A C is perpendicular to the base B Cdot

Fill in the blanks in the following so that each of the following statements is true Sides opposite to equal angles of a triangle are ....... Angle opposite to equal sides of a triangle are ....... In an opposite to equal sides of a triangle are ....... In a A B C if /_A=/_C , then A B= ..... If altitudes C E a n d B F of a triangle A B C are equal, then A B= ........ In an isosceles triangle A B C with A B=A C , if B D a n d C E are its altitudes, then B D is .......... C E In right triangles A B C a n d D E F , if hypotenuse A B=E F and side A C=D E , then A B C ~= ....