NCERT Mathematics Class 10 Exemplar Ch 6 Triangles Part 7 (For CBSE, ICSE, IAS, NET, NRA 2022)

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

ABC is a Triangle Right Angled at B

Answer:

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

PQR is a Right Triangle Right Angled at Q

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

6.20, L Parallel M and Line Segments AB, CD and EF

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

PA, QB, RC and SD Are All Perpendiculars

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 .]

DF Intersect the Side AC of a Triangle ABC

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.