Mathematics for Class 9>Chapter 8 - Quadrilaterals>EXERCISE 8.2>Q 2

MEDIUM

9th Manipur Board

IMPORTANT

Earn 100

Prove that the quadrilateral formed by joining the midpoints of the sides of a rhombus is a rectangle.

Important Questions on Quadrilaterals

MEDIUM

9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 8 - Quadrilaterals>EXERCISE 8.2>Q 3

If there are three parallel lines and the intercepts made by them on a transversal are equal in length, prove that the intercepts on any other transversal are equal in length, prove that the intercepts on any other transversal are also equal in length.

MEDIUM

9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 8 - Quadrilaterals>EXERCISE 8.2>Q 4

In

△ A B C, D, E

and

F

are midpoints of the sides

A B, B C

and

C A

respectively. Show that

△ A B C

is divided into four congruent triangles by joining

D, E

and

F

.

MEDIUM

9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 8 - Quadrilaterals>EXERCISE 8.2>Q 5

A B C D

is a rectangle and

P, Q, R, S

are mid-points of the sides

A B, B C, C D

and

D A

respectively. Show that the quadrilateral

P Q R S

is a rhombus.

MEDIUM

9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 8 - Quadrilaterals>EXERCISE 8.2>Q 6

A B C D

is a trapezium in which

A B ∥ D C

,

B D

is a diagonal and

E

is the midpoint of

A D

. A line is drawn through

E

parallel to

A B

intersecting

B C

at

F

. Show that

F

is the midpoint of

B C

.

MEDIUM

9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 8 - Quadrilaterals>EXERCISE 8.2>Q 7

Show that the line segment joining the midpoints of the opposite sides of a quadrilateral bisect each other.

MEDIUM

9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 8 - Quadrilaterals>EXERCISE 8.2>Q 8

A B C

is a triangle right-angled at

C

. A line through the midpoint

M

of the hypotenuse

A B

and parallel to

B C

intersects

A C

at

D

. Show that

D

is midpoint of

A C

.

MEDIUM

9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 8 - Quadrilaterals>EXERCISE 8.2>Q 8

A B C

is a triangle right-angled at

C

. A line through the mid-point

M

of the hypotenuse

A B

and parallel to

B C

intersects

A C

at

D

. Show that

M D ⊥ A C

.

MEDIUM

9th Manipur Board

IMPORTANT

Mathematics for Class 9>Chapter 8 - Quadrilaterals>EXERCISE 8.2>Q 8

A B C

is a triangle right-angled at

C

. A line through the mid-point

M

of the hypotenuse

A B

and parallel to

B C

intersects

A C

at

D

. Show that

C M = M A = \frac{1}{2} A B

.