Maths
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 [...]
6. ABC is a right triangle with AB = AC. Bisector of ∠A meets BC at D. Prove that BC = 2 AD.
30
Jun
6. ABC is a right triangle with AB = AC. Bisector of ∠A meets BC at D. Prove that BC = 2 AD. 6. ABC is a right triangle with AB = AC. Bisector of ∠A meets BC at D. Prove that BC = 2 AD. June 30, 2021 Category: Chapter 7 - Triangles , [...]
5. ABCD is a quadrilateral in which AB = BC and AD = CD. Show that BD bisects both the angles ABC and ADC.
30
Jun
5. ABCD is a quadrilateral in which AB = BC and AD = CD. Show that BD bisects both the angles ABC and ADC. 5. ABCD is a quadrilateral in which AB = BC and AD = CD. Show that BD bisects both the angles ABC and ADC. June 30, 2021 Category: Chapter 7 - [...]
4. P is a point on the bisector of ∠ABC. If the line through P, parallel to BA meet BC at Q, prove that BPQ is an isosceles triangle.
30
Jun
4. P is a point on the bisector of ∠ABC. If the line through P, parallel to BA meet BC at Q, prove that BPQ is an isosceles triangle. 4. P is a point on the bisector of ∠ABC. If the line through P parallel to BA meet BC at Q prove that BPQ is [...]