Chapter 8: Similar Triangles

Exercise - 13

1. In the adjoing figure, If

AB = x units CD = y units and PQ = Z units, Prove that ,

2. In a and Q are point on the side AB and AC respectively such that PQ is parallel to BC. Prove that median AD drawn from A to BC, bisect PQ.

3. 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.

4. 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

5. 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

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

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

8. In is aculte, BD and CE are perenducular on AC and AB respectively. Prove that AB X AE = AC X AD

9. Through the vertex D of a parallotogram ABCD, a line is drawn to intersect the sides AB and CB produced at E and F respectively prove that:

10. 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.

11. 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

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

13. 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.

Theorem 2. The ratio of the ares of two similar triangles is equal to the ratio of the squares of their corresponding sides.

Given:-

To prove:

Construction: and are drawn as in figure

proof:-

Or,

Now in and PSQ,

Hence,