Chapter 7 – Triangles
21. ABCD is quadrilateral such that AB = AD and CB = CD. Prove that AC is the perpendicular bisector of BD.
30
Jun
21. ABCD is quadrilateral such that AB = AD and CB = CD. Prove that AC is the perpendicular bisector of BD. 21. ABCD is quadrilateral such that AB = AD and CB = CD. Prove that AC is the perpendicular bisector of BD. June 30, 2021 Category: Chapter 7 - Triangles , Maths , [...]
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.
30
Jun
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. 20. Prove that in a triangle angle opposite the longest side is greater than 2/3 of a right angle. other than an equilateral triangle June 30, 2021 Category: Chapter 7 - [...]
19. AB and CD are the smallest and largest sides of a quadrilateral ABCD. Out of ∠B and ∠D decide which is greater.
30
Jun
19. AB and CD are the smallest and largest sides of a quadrilateral ABCD. Out of ∠B and ∠D decide which is greater. 19. AB and CD are the smallest and largest sides of a quadrilateral ABCD. Out of ∠B and ∠D decide which is greater. June 30, 2021 Category: Chapter 7 - Triangles , [...]
18. ABC is a right triangle such that AB = AC and bisector of angle C intersects the side AB at D. Prove that AC + AD = BC.
30
Jun
18. ABC is a right triangle such that AB = AC and bisector of angle C intersects the side AB at D. Prove that AC + AD = BC. 18. ABC is a right triangle such that AB = AC and bisector of angle C intersects the side AB at D. Prove that AC + [...]
17. ABCD is a quadrilateral such that diagonal AC bisects the angles A and C. Prove that AB = AD and CB = CD.
30
Jun
17. ABCD is a quadrilateral such that diagonal AC bisects the angles A and C. Prove that AB = AD and CB = CD. 17. ABCD is a quadrilateral such that diagonal AC bisects the angles A and C. Prove that AB = AD and CB = CD. June 30, 2021 Category: Chapter 7 - [...]
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 AD = BC.
30
Jun
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 AD = BC. 16. Line segment joining the mid-points M and N of parallel sides AB and DC respectively of a trapezium ABCD is [...]
15. Two lines l and m intersect at the point O and P is a point on a line n passing through the point O such that P is equidistant from l and m. Prove that n is the bisector of the angle formed by l and m.
30
Jun
15. Two lines l and m intersect at the point O and P is a point on a line n passing through the point O such that P is equidistant from l and m. Prove that n is the bisector of the angle formed by l and m. 1. Find all the angles of an [...]
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.
30
Jun
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. 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. June 30, 2021 Category: Chapter 7 - Triangles , [...]
13. In a triangle ABC, D is the mid-point of side AC such that BD = 1/2 AC. Show that ∠ABC is a right angle.
30
Jun
13. In a triangle ABC, D is the mid-point of side AC such that BD = 1/2 AC. Show that ∠ABC is a right angle. 13. In a triangle ABC D is the mid-point of side AC such that BD = 1/2 AC. Show that ∠ABC is a right angle. June 30, 2021 Category: Chapter [...]
11. Show that in a quadrilateral ABCD, AB + BC + CD + DA < 2 (BD + AC)
30
Jun
11. Show that in a quadrilateral ABCD, AB + BC + CD + DA