MEDIUM
9th Manipur Board
IMPORTANT
Earn 100

P is a point equidistant from two lines l and m intersecting at a point A. Prove that the line AP bisects the angle between the lines. 

Important Questions on Triangles

MEDIUM
9th Manipur Board
IMPORTANT
Mathematics for Class 9>Chapter 7 - Triangles>EXERCISE 7.1>Q 11
ABCD is a rectangle. P, Q, R and S are the mid-points of AB, BC, CD and DA respectively. Prove that PQRS is a rhombus. 
HARD
9th Manipur Board
IMPORTANT
Mathematics for Class 9>Chapter 7 - Triangles>EXERCISE 7.1>Q 12
Prove that the diagonals of a rhombus bisect each other at right angles. 
MEDIUM
9th Manipur Board
IMPORTANT
Mathematics for Class 9>Chapter 7 - Triangles>EXERCISE 7.1>Q 13
ABCD is a parallelogram and AC is one of its diagonals. Prove that ∆ABC≅∆ADC.
MEDIUM
9th Manipur Board
IMPORTANT
Mathematics for Class 9>Chapter 7 - Triangles>EXERCISE 7.1>Q 14
AB and AC are equal sides of an isosceles ∆ABC. If the bisectors of ∠ABC and ∠ACB intersect each other at O, prove ∆AOB≅∆AOC. 
HARD
9th Manipur Board
IMPORTANT
Mathematics for Class 9>Chapter 7 - Triangles>EXERCISE 7.1>Q 15

The image of an object placed at a point A before a plane mirror LM is seen at the point B by an observer at D as in the adjoining figure. Prove that the image is as far behind the mirror as the object is in front of the mirror.

Question Image  

MEDIUM
9th Manipur Board
IMPORTANT
Mathematics for Class 9>Chapter 7 - Triangles>EXERCISE 7.2>Q 1
If the altitudes of a triangle are equal, prove that the triangle is equilateral.
MEDIUM
9th Manipur Board
IMPORTANT
Mathematics for Class 9>Chapter 7 - Triangles>EXERCISE 7.2>Q 2
If perpendiculars from any point within an angle on its arms are congruent, prove that the point lies on the bisector of that angle.
MEDIUM
9th Manipur Board
IMPORTANT
Mathematics for Class 9>Chapter 7 - Triangles>EXERCISE 7.2>Q 3
The diagonals AC and BD of a rhombus ABCD bisect each other at right angles at O. Prove that ∆AOB≅∆COD.