# NCERT Mathematics Class 10 Exemplar Ch 6 Triangles Part 7

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9. In Fig. 6.18, ABC is a triangle right angled at B and . If , and , find BD and AB.

Answer:

10. In Fig. 6.19, PQR is a right triangle right angled at Q and . If and , find QS, RS and QR.

Answer:

11. In Δ PQR, such that D lies on QR . If and , prove that

12. In a quadrilateral ABCD, . Prove that [Hint: Produce AB and DC to meet at E.]

13. In fig. 6.20, l || m and line segments AB, CD and EF are concurrent at point P. Prove that

14. In Fig. 6.21, PA, QB, RC and SD are all perpendiculars to a line l, , , and . Find PQ, QR and RS.

Answer:

15. O is the point of intersection of the diagonals AC and BD of a trapezium ABCD with . Through O, a line segment PQ is drawn parallel to AB meeting AD in P and BC in Q. Prove that .

16. In Fig. 6.22, line segment DF intersect the side AC of a triangle ABC at the point E such that E is the mid-point of CA and . Prove that . [Hint: Take point G on AB such that .]

17. Prove that the area of the semicircle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the semicircles drawn on the other two sides of the triangle.

18. Prove that the area of the equilateral triangle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the equilateral triangles drawn on the other two sides of the triangle.