Games and Sports

10.1
1. In the figure, CD is the perpendicular bisector of AB, prove that ΔADC = ΔBDC.
2. In the figure, CD = CB and ∠DCA= ∠BCA.
Prove that AB = AD.
3. In the figure ∠BAC= ∠ACD and AB= DC.
Prove that AD= BC, ∠CAD = ∠ACD and
∠ADC= ∠ABC.
4. If the base of an isosceles triangles are produced both ways, show that the exterior angles so formed are equal.
5. In the figure, AD= AE, BD= CE and ∠AEC=∠ADB.
Prove that AB = AC.
6. In the figure, ΔABC and ΔDBC are both isosceles triangles. Prove that, ΔABD = ACD.
7. Show that the medians drawn from the extremities of the base of an isosceles triangle to the opposite sides are equal to one another.
8. Prove that the angles of an equilateral triangle are equal to one another.
10.2
1. In the ΔABC, AB = AC and O is an interior point of the ΔABC such that OB =
OC. Prove that ∠AOB= ∠AOC.
2. In the ΔABC, D and E are points on AB and AC respectively such that BD = CE and BE = CD. Prove that ∠ABC = ∠ACB.
3. In the figure ΔABC, AB = AC,BD = DC and
BE = CF . Prove that ∠EDB = ∠FDC .
4. In the figure, ABC is a triangle in which AB =
AC, ∠BAD= ∠CAE. Prove that AD = AE.
5. In the quadrilateral ABCD, AC is the bisector of the ∠BAD and ∠BCD. Prove that ∠B = ∠D.
6. In the figure, the sides AB and CD of a quadrilateral ABCD are equal and parallel and the diagonals AC and BD intersect at the point
O. Prove that AD = BC.
7. Prove that, the perpendiculars from the end points of the base of an isosceles triangle to the opposite sides are equal.
8. Prove that, if the perpendiculars from the end points of the base of a triangle to the opposite sides are equal then the triangle is an isosceles triangle.
9. In the quadrilateral ABCD, AB = AD and ∠B = ∠D = 1 right angle. Prove that
ΔABC