triangle and its popperties

The triangle and its Properties

1.      The angles of triangles are in the ratio 1:2:3. Determine the corresponding angles.

2.      Which of the following triplets can be angles of a triangle?

i.                    76^o, 64 ^o, 40 ^o                                  ii.           56 ^o, 62 ^o, 62 ^o

3.      Two angles of triangle are of measures 60^o and 75 ^o. find the measure of the third angle.

4.      One of the acute angles of a right angled triangle is 42 ^o. find the other acute angle.

5.      Two acute angles of a right angled triangle are equal. Find the two angles.

6.      In the given five sided closed figure, find ∠EAB+ ∠ABC+ ∠BCD+ ∠CDE+ ∠DEA

7.      The angles of a triangle are in the ratio 5:4:3. Find the measure of each angle.

8.      One side of a triangle is produced and the exterior angle so formed is 120^o. if the interior opposite angles are in the ratio 2:3, find the measure of each angle of the triangle.

9.      If the sides of a triangle are produced in order, prove that the sum of the exterior angles so formed is 360^o.

10.  In the figure given below find the value of x and y

11.  In △PRQ side QR is extended to S. if ∠PRS=150 ^o and RP=RQ, find the three angles of △PRQ

12.  AM is a median of a △ABC. Prove that AB+BC+CA>2AM

13.  Find the length of the diagonal of a rectangle having sides 16cm and 12cm.

14.  ABC is a triangle, right angled at C. If AB=25cm and AC=7cm, find BC

15.  A 10m long ladder reached a window 8m high from the ground on placing it against a wall at a distance x. find the distance x?

16.  Identify the Pythagorean triplets from the following:

i.                    3,7,9                   ii.           7,24,25                             iii.          4,5,7