Show that in an isosceles triangle, angles opposite to equal sides are equal.

In an isosceles triangle, prove that the angles opposite to equal sides are equal.

Figure, shows a kite in which BCD is the shape of a quadrant of a circle of radius 42cm. ABCD is a square and CEF is an isosceles right angled triangle whose equal side are 6cm long. Find the area of the shaded region.

If a line is drawn parallel to the base of an isosceles triangle to intersect its equal sides, prove that the quadrilateral, so formed is cyclic.

Find the area of an isosceles triangle in which each of the equal sides measures 30 cm and the third side is 48 cm long

Find the area of an isosceles triangle which has base 12 cm and equal sides are 10 cm each.

Which of the following statements are true (T) and which are false (F): Side opposite to equal angles of a triangle may be unequal. Angle opposite to equal sides of a triangle are equal. The measure of each angle of an equilateral triangle is 60^0 If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles. The bisectors of two equal angles of a triangle are equal. If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles. The two altitudes corresponding to two equal sides of a triangle need not be equal. If any two sides of a right triangle are respectively equal to two sides of other right triangle, then the two triangles are congruent. Two right triangles are congruent if hypotenuse and a side of one triangle are respectively equal to the hypotenuse and a side of the other triangle.

Fill in the blanks in the following so that each of the following statements is true. (i) Sides opposite to equal angles of a triangle are ....... (ii) Angle opposite to equal sides of a triangle are ....... (iii) In an equilateral triangle all angles are ....... (iv) In a A B C if /_A=/_C , then A B=\ ..... (v) If altitudes C E\ a n d\ B F of a triangle A B C are equal, then A B= ........ (vi) 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 . (vii) 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\ ~= ....

The base of an isosceles triangle is 16 cm. If both the equal sides be 17 cm each, find the area of the triangle.

Find the area of an isosceles right triangle. If one of the equal sides is 20 cm long.

Find the area of an isosceles triangle whose equal sides are 5 cm each and base is 6 cm.