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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
10. Prove that sum of any two sides of a triangle is greater than twice the median with respect to the third side.
30
Jun
10. Prove that sum of any two sides of a triangle is greater than twice the median with respect to the third side. 10. Prove that sum of any two sides of a triangle is greater than twice the median with respect to the third side. June 30, 2021 Category: Chapter 7 - Triangles , [...]
9. ABC is an isosceles triangle in which AC = BC. AD and BE are respectively two altitudes to sides BC and AC. Prove that AE = BD.
30
Jun
9. ABC is an isosceles triangle in which AC = BC. AD and BE are respectively two altitudes to sides BC and AC. Prove that AE = BD. 9. ABC is an isosceles triangle in which AC = BC. AD and BE are respectively two altitudes to sides BC and AC. Prove that AE = [...]
8. ABC and DBC are two triangles on the same base BC such that A and D lie on the opposite sides of BC, AB = AC and DB = DC. Show that AD is the perpendicular bisector of BC.
30
Jun
8. ABC and DBC are two triangles on the same base BC such that A and D lie on the opposite sides of BC, AB = AC and DB = DC. Show that AD is the perpendicular bisector of BC. 8. ABC and DBC are two triangles on the same base BC such that A [...]
7. O is a point in the interior of a square ABCD such that OAB is an equilateral triangle. Show that ∆ OCD is an isosceles triangle.
30
Jun
7. O is a point in the interior of a square ABCD such that OAB is an equilateral triangle. Show that ∆ OCD is an isosceles triangle. 7. O is a point in the interior of a square ABCD such that OAB is an equilateral triangle. Show that ∆ OCD is an isosceles triangle. June [...]