# NCERT Mathematics Class 9 Exemplar Ch 7 Triangles Part 7

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Q.11. Show that in a quadrilateral ABCD,

Q.12. Show that in a quadrilateral ABCD,

Q.13. In a triangle ABC, D is the mid-point of side AC such that Show that ∠ ABC is a right angle.

Q.14. In a right triangle, prove that the line-segment joining the mid-point of the hypotenuse to the opposite vertex is half the hypotenuse.

Q.15. Two lines l and m intersect at the point O and P is a point on a line in passing through the point of such that P is equidistant from l and m. Prove that n is the bisector of the angle formed by l and m.

Q.16. Line segment joining the mid-points M and N of parallel sides AB and DC, respectively of a trapezium ABCD is perpendicular to both the sides AB and DC. Prove that

Q.17. ABCD is a quadrilateral such that diagonal AC bisects the angles A and C. Prove that and

Q.18. ABC is a right triangle such that and bisector of angle C intersects the side AB at D. Prove that

Q.19. AB and CD are the smallest and largest sides of a quadrilateral ABCD. Out of ∠B and ∠ D decide which is greater.

Answer: ∠B will be greater.

Q.20. Prove that in a triangle, other than an equilateral triangle, angle opposite the longest side is greater than 2/3 of a right angle.

Q.21. ABCD is quadrilateral such that and Prove that AC is the perpendicular bisector of BD.