MEDIUM
9th CBSE
IMPORTANT
Earn 100

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

Important Questions on Triangles

MEDIUM
9th CBSE
IMPORTANT
NCERT Exemplar Mathematics - Class 9>Chapter 7 - Triangles>Exercise>Q 6
ABC is a right triangle with AB=AC. Bisector of ∠A meets BC at D. Prove that BC=2AD.
HARD
9th CBSE
IMPORTANT
NCERT Exemplar Mathematics - Class 9>Chapter 7 - Triangles>Exercise>Q 7
O is a point in the interior of a square ABCD such that OAB is an equilateral triangle. Show that ΔOCD is an isosceles triangle.
HARD
9th CBSE
IMPORTANT
NCERT Exemplar Mathematics - Class 9>Chapter 7 - Triangles>Exercise>Q 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.
HARD
9th CBSE
IMPORTANT
NCERT Exemplar Mathematics - Class 9>Chapter 7 - Triangles>Exercise>Q 9
ABC is an isosceles triangle in which AC=BC. AD and BE are respectively two altitudes to the sidesBC and AC. Prove that AE=BD.
HARD
9th CBSE
IMPORTANT
NCERT Exemplar Mathematics - Class 9>Chapter 7 - Triangles>Exercise>Q 10
Prove that sum of any two sides of a triangle is greater than twice the median with respect to the third side.
MEDIUM
9th CBSE
IMPORTANT
NCERT Exemplar Mathematics - Class 9>Chapter 7 - Triangles>Exercise>Q 11
Show that in a quadrilateral ABCD, AB+BC+CD+DA<2(BD+AC).
MEDIUM
9th CBSE
IMPORTANT
NCERT Exemplar Mathematics - Class 9>Chapter 7 - Triangles>Exercise>Q 12

Show that in a quadrilateral ABCD. AB+BC+CD+DA>AC+BD

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MEDIUM
9th CBSE
IMPORTANT
NCERT Exemplar Mathematics - Class 9>Chapter 7 - Triangles>Exercise>Q 13
In a triangle ABC, D is the midpoint of side AC such that BD=12AC. Show that ∠ABC is a right angle.