Triangles-Test

Total time 45 min

Total Marks : 30

1.  ABCD is a parallelogram. If the two diagonals are equal, find the measure of ∠ABC.

(2 Marks)

2.  In the figure below, ABC is a triangle in which AB = AC. X and Y are points on AB and AC such that AX = AY. Prove that ΔABY ≌ ΔACX.

(2 Marks)

3.  In ΔABC and ΔADC, AB = AD and BC = CD. Prove that ∠ABC ≌ ΔADC.

(2 Marks)

4.  In the given figure, AC = BC, ∠DCA = ∠ECB and ∠DBC = ∠EAC. Prove that ΔDBC ≌ ΔEAC and DC = EC.

(3 Marks)

5.  In ΔABC, AB = AC and the bisector of angles B and C intersect at point O. Prove that BO = CO and AO bisects ∠BAC.

(3 Marks)

6.  Show that a median of a triangle divides it into two triangles of equal areas.

(3 Marks)

7.  In a right angled triangle, one acute angle is double the other. Prove that the hypotenuse is double the smallest side.

(3 Marks)

8.  Prove that angles opposite to equal sides of an isosceles triangle are equal.

(4 Marks)

9.  In the given figure, ΔXYZ and ΔPYZ are two isosceles triangle on the same base YZ with XY = XZ and PY = PZ. If ∠P = 120�X and ∠XYP = 40�X, then find ∠YXZ.

(4 Marks)

10.  A point O is taken inside an equilateral four sides figure ABCD such that its distances from the angular points D and B are equal. Show that AO and OC are in one and the same straight line.

(4 Marks)