Quadrilaterals

Quadrilaterals

by students of class IX A

The sum of the angles of a quadrilateral is 360

​Angle Sum Property

Multiple Choice

Three angles of a quadrilateral are equal and the fourth angle is equal to 137°. Find each of the equal angles of the quadrilateral.

• 25

• 22

• 23

• 27

Types of Quadrilaterals and their Properties

​Trapezium

One pair of opposite sides of a trapezium is parallel

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Diagonals bisect each other​

​Parallelogram

​Diagonal of a parallelogram divides it into 2 congruent triangles.

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Opposite sides of a parallelogram are equal

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Opposite angles of a parallelogram are equal.

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Diagonals of a parallelogram bisect each other

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 if a pair of opposite sides are equal and parallel then the quadrilateral is a parallelogram.

Multiple Choice

In the given figure, ABCD is a parallelogram. If ∠B = 100°, then find the value of ∠A +∠C.

• 150

• 160

• 120

• 170

​Kite

​Two pairs of adjacent sides are equal

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Diagonals are perpendicular bisectors of each other

​Rectangle

​It is a parallelogram where all the angles are right angles

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​Opposite sides are equal

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​Opposite sides are parallel

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Diagonals are equal

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Diagonals bisect each other

​Rhombus

​It is a parallelogram where all sides are equal

Opposite sides are parallel

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Opposite angles are equal

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Diagonals of a rhombus are perpendicular bisectors of each other

​Square

​It is a parallelogram where all sides are equal

All angle are right angles

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Opposite sides are parallel

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Diagonals are equal

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Diagonals are perpendicular bisectors of each other

Multiple Choice

If angles A, B, C and D of the quadrilateral ABCD, taken in order, are in the ratio 3:7:6:4, then ABCD is a

• Rhombus

• Rectangle

• Parallelogram

• Trapezium

Multiple Choice

If ABCD is a trapezium in which AB || CD and AD = BC, then:

• ∠A = ∠B

• ∠A < ∠B

• ∠A > ∠B

• None of the above

Multiple Choice

In the given figure, ABCD is a parallelogram in which ∠DAB = 70 and ∠DBC = 65, then find the measure of ∠CDB

• 40

• 45

• 36

• 30

​Midpoint Theorem

​The line segment joining the midpoints of 2 sides of a triangle is half of the 3rd side and parallel to it.

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​The converse of the midpoint theorem states that ” if a line is drawn through the midpoint of one side of a triangle, and parallel to the other side, it bisects the third side”

Multiple Choice

The quadrilateral formed by joining the mid points of the sides of a quadrilateral ABCD taken in order, is a rectangle if:

• ABCD is a parallelogram

• AC = BD

• ABCD is a right angle triangle

• Diagonals AC and BD are perpendicular

THANK YOU SO MUCH!!!​