CBSE Class 10 Maths Similar Triangles

Chapter 8

Similar Triangles

Similar Triangles:

Whenever we talk about two congruent figures then they have the ‘same shape’ and the ‘same size’. There are figures that are of the ‘same shape but not necessarily of the ‘same size’. They are said to be similar. Congruent figures are similar but the converse is not true

All regular polygons of same number of sides are similar. They are equilateral triangles, squares etc. All circles are also similar.

Two polygons of the same number of sides are similar if their corresponding angles are sides are proportional.

Two triangles are similar if their corresponding are equal and corresponding sides are proportional.

Exercise

1. Through the mid-point M of the side CD of a parallelogram AB CD, the line BM is drawn intersecting AC in L and AD produced in E. Prove that EL = 2BL.

2. ABC is a triangle right anlgled at C. If P is the length of perpendicular from C to AB and AB = c, BC = a and CA = b, show that pc = ab

3. Two right angles ABC and DBC are drawn on the same hypoeuuge BC and on the same side of BC. If AC and BD interscta at P, prove that AP X PC = BP X PD

4. The perimeter of two smilar triangles ABC and PQR are respectively 32cm and 24cm.If PQ = 12cm, find AB.

5. In a right triangles ABC, the perpendicular BD on the hypotenuse Ac is drown. Prove that AC X CD = BC2

6. Two sides and a mediam bisecting one of these sides of a triangle are respectively proportional to the two sides and the corresponding mediam of the other triangle. Prove that the triangles are similar.

7. If the angles of one triangles are respectively equal to the angles of another tranles. Prove that the ratio of their corresponding sides is the same as the ratio of their corresponding.

1. medians

2. altitudes

3. angle bisectors

8. E is a point on side AD produced of a parallelogram ABCD and BE intersects CD at F. prove that

9. If a perpecdicular is drawn from the vertex of the right angles of a right triangles to the hypoteuuse, the triangles on each side of the perpendicular are similar to the whole triangles and to each other.

Please refer to attached file for CBSE Class 10 Maths Similar Triangles