Quadrila terals Presented By :- PAWAN SINGH T.G.T(Maths) K.V. NO.2 AFS Suratgarh 2 nd spell inservice course
Quadrilaterals
Presented By :-
PAWAN SINGH T.G.T(Maths) K.V. NO.2 AFS Suratgarh
2nd spell inservice course
LEARNING Objective's
• Definition of Quadrilateral.• Types of Quadrilateral.• Difference between
Rhombus & Square and Trapezoid &Parallelogram.
• Angle sum property of Quadrilateral.
Game between three players
One player join them
Definition:-
“A Quadrilateral is polygon with four sides. And A polygon is a closed shape consisting of line segments that has at least three sides. “
OR
“A flat closed shape with four straight sides is called Quadrilaterals“
•A quadrilaterals has four sides, four angles and four vertices.
“Quad” means four. Why would all of these shapes be called “quadrilaterals”?
Each shape has four sides.
Quadrilaterals
Square• A square has four sides that are each
the same length. • It also has four right angles (perfect
corners).
1
2 3
4
Rhombus• A rhombus has four sides
that are each the same length.
• But it has two acute and two obtuse angles.
acute
acuteobtuse
obtuse
Square and Rhombus
• A square and a rhombus both have four sides that are the same length. So, how are they different?
Square and Rhombus• A rhombus can be thought
of as a slanted square.• If we push on the left-hand
side of this square, it might end up looking like…
a rhombus.
The only difference between a square and a rhombus is their angles.
Trapezoid• A trapezoid has four sides. • Two sides are parallel. • The opposing two sides are
not parallel.
Those are parallel.
Those are not parallel.
Rectangle•A rectangle has four sides – two long sides and two short sides.
•Two sides are parallel.
•The opposing two sides are also parallel.
•It also has four right angles.
Parallelogram•A parallelogram has four sides – two long sides and two short sides.
•Opposite sides are parallel.
•But, it has two acute and two obtuse angles.
Rectangle and Parallelogram• A parallelogram can be
thought of as a slanted rectangle.
• If we push on the left-hand side of this rectangle, it might end up looking like… a parallelogram.
The only difference between a rectangle and a parallelogram is their angles.
COMPARISION OF QUADRILATERALS.
Square All sides are equal & parallel
Each angle 90°
Rhombus All sides are equal & parallel
2 angles acute & 2 obtuse.
Trapezoid One pair of opposite sides is parallel
2 angles acute & 2 obtuse
Parallelogram Both pair of opposite sides is parallel
2 angles acute & 2 obtuse
RHOMBUS
RECTANGLE
SQUARE
Angle sum Property of a Quadrilateral• Let ABCD be a quadrilateral and A & C joined to get
diagonal AC. We obtain two triangles ∆ ADC & ∆ ABCUsing Angle sum property in ∆ADC DAC + ACD + D = 180° ----------------- (1)
Similarly, in ∆ ABC
CAB + ACB + A = 180° ---------------- (2)
Adding (1) and (2) we get
DAC + ACD+ D + CAB + ACB + B = 180° + 180°
Also, DAC + CAB = A and ACD + ACB = C
SO A + B + C + D =360°
The sum of the angles of a quadrilateral is 360°
Sample problem• The angles of quadrilateral are in the ratio
3:5:9:13.Find all the angles of the quadrilateral.• Sol‘n:-Let the angles are 3k,5k,9k&13 (multiple of
k) We know Sum of angles is equal to 360° . So 3k+5k+9k+13k = 360° Or 30k = 360° Or k= 360° /30 Or k=12 Thus angle of quadrilateral are 36°,60°,108 ° & 156.°
•
Evaluation
• Quadrilateral whose two opposite sides are parallel is called ………….
• Trapezoid has ……. Pair of parallel sides.
• Polygon has ………or more sides.• The sum of angles in a quadrilateral is
……• If the angles of parallelogram is in ratio
1:2:1:2. Find the angles‽