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Triangles

Show that in a quadrilateral ABCD, AB + BC + CD + DA < 2 (BD + AC)

05/11/2024

Mathematics

9th

Triangles

Prove that sum of any two sides of a triangle is greater than twice the median with respect to the third side.

05/11/2024

Mathematics

9th

Triangles

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.

05/11/2024

Mathematics

9th

Triangles

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

05/11/2024

Mathematics

9th

Triangles

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.

05/11/2024

Mathematics

9th

Triangles

ABC is a right triangle with AB = AC. Bisector of ∠A meets BC at D. Prove that BC = 2 AD.

05/11/2024

Mathematics

9th

Triangles

ABCD is a quadrilateral in which AB = BC and AD = CD. Show that BD bisects both the angles ABC and ADC

05/11/2024

Mathematics

9th

Triangles

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.

05/11/2024

Mathematics

9th

Triangles

Find all the angles of an equilateral triangle.

05/11/2024

Mathematics

9th

Triangles

S is any point in the interior of ∆ PQR. Show that SQ + SR < PQ + PR.

05/11/2024

Mathematics

9th