QUADRILATERALS

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DEEPAK SHARMA KAPIL GYANPEETH MATHEMATICS

ACTIVITY:

ACTIVITY The fold crease QUADRILATERALS Parallelogram

ACTIVITY:

QUADRILATERALS ACTIVITY

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Parallelograms Now, Let’s review what we learned last class

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A quadrilateral is a PARALLELOGRAM if and only if it has two sets of parallel sides

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Properties 1.BOTH pairs of opposite sides are parallel 2.BOTH pairs of opposite sides are congruent 3. BOTH pairs of opposite angles are congruent 4.Consecutive angles are supplementary 5.diagonals BISECT each other

ACTIVITY:

QUADRILATERALS RECTANGLE 1. Opposite sides parallel. 2. Opposite sides congruent. 3. Opposite angles are congruent. 4. Consecutive angles are supplementary. 5. Diagonals bisect each other. ACTIVITY

ACTIVITY:

QUADRILATERALS 1. Opposite sides parallel. 2. Opposite sides congruent. 3. Opposite angles are congruent. 4. Consecutive angles are supplementary. 5. Diagonals bisect each other. ACTIVITY

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RECTANGLE A parallelogram with FOUR RIGHT ANGLES

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A quadrilateral is a RECTANGLE if and only if it has four right angles

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RECTANGLE Diagonals are Congruent

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QUADRILATERALS RHOMBUS 1. Has 4 right angles. 2. Diagonals are congruent. 3. All properties of parallelogram. 1. Opposite sides parallel. 2. Opposite sides congruent. 3. Opposite angles are congruent. 4. Consecutive angles are supplementary. 5. Diagonals bisect each other. ACTIVITY

ACTIVITY:

QUADRILATERALS 1. Opposite sides parallel. 2. Opposite sides congruent. 3. Opposite angles are congruent. 4. Consecutive angles are supplementary. 5. Diagonals bisect each other. 1. Has 4 right angles. 2. Diagonals are congruent. 3. All properties of parallelogram. ACTIVITY

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RHOMBUS A parallelogram with FOUR CONGRUENT SIDES

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A quadrilateral is a RHOMBUS if and only if it has four congruent sides

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RHOMBUS Diagonals Bisect A Pair of Opposite Angles

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Diagonals are Perpendicular RHOMBUS

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QUADRILATERALS SQUARE 1. Has 4 Congruent sides 2. Diagonals bisect opposite angles. 3. Diagonals are perpendicular. 4. All properties of parallelograms. 1. Opposite sides parallel. 2. Opposite sides congruent. 3. Opposite angles are congruent. 4. Consecutive angles are supplementary. 5. Diagonals bisect each other. 1. Has 4 right angles. 2. Diagonals are congruent. 3. All properties of parallelogram. ACTIVITY

ACTIVITY:

QUADRILATERALS 1. Opposite sides parallel. 2. Opposite sides congruent. 3. Opposite angles are congruent. 4. Consecutive angles are supplementary. 5. Diagonals bisect each other. 1. Has 4 right angles. 2. Diagonals are congruent. 3. All properties of parallelogram. 1. Has 4 Congruent sides 2. Diagonals bisect opposite angles. 3. Diagonals are perpendicular. 4. All properties of parallelograms. ACTIVITY

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A quadrilateral is a SQUARE if and only if it has four congruent sides and four right angles

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SQUARE A parallelogram with FOUR RIGHT ANGLES AND FOUR CONGRUENT SIDES

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Holds same properties as Rhombus and Rectangle SQUARE

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QUADRILATERALS 1. 4 congruent sides and 4 congruent (right) angles 2. All properties of parallelogram, rectangle, and rhombus TRAPEZOID KITE 1. Opposite sides parallel. 2. Opposite sides congruent. 3. Opposite angles are congruent. 4. Consecutive angles are supplementary. 5. Diagonals bisect each other. 1. Has 4 right angles. 2. Diagonals are congruent. 3. All properties of parallelogram. 1. Has 4 Congruent sides 2. Diagonals bisect opposite angles. 3. Diagonals are perpendicular. 4. All properties of parallelograms. ACTIVITY

ACTIVITY:

QUADRILATERALS 1. Opposite sides parallel. 2. Opposite sides congruent. 3. Opposite angles are congruent. 4. Consecutive angles are supplementary. 5. Diagonals bisect each other. 1. Has 4 right angles. 2. Diagonals are congruent. 3. All properties of parallelogram. 1. Has 4 Congruent sides 2. Diagonals bisect opposite angles. 3. Diagonals are perpendicular. 4. All properties of parallelograms. 1. 4 congruent sides and 4 congruent (right) angles 2. All properties of parallelogram, rectangle, and rhombus ACTIVITY

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Trapezoid ONE PAIR OF PARALLEL SIDES

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A quadrilateral is a TRAPEZOID if and only if it has ONE pair of parallel sides

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Trapezoid leg leg base base Leg angles are supplementary Leg angle 1 Leg angle 2

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Trapezoid Base (b 2 ) Base (b 1 ) Midsegment is ½ the sum of the lengths of the bases Midsegment =½ (b 1 + b 2 )

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Trapezoid leg leg base base Isosceles: Base angles are congruent Base angle 2 Base angle 1

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Trapezoid Isosceles: Diagonals are congruent

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KITE TWO PAIRS OF CONSECUTIVE CONGRUENT SIDES (opposite sides not congruent)

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A quadrilateral is a KITE if and only if it has two pairs of congruent consecutive sides

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KITE Diagonals are perpendicular

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KITE Short diagonal is bisected

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KITE ONE pair of opposite angles are congruent (not both)

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KITE The other angles are bisected by the diagonal

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QUADRILATERALS 1. One pair of parallel sides 2. Leg angles supplementary 3. Midsegment= ½(b 1 + b 2 ) 4. Isosceles—see back 1. 2 pairs of consecutive sides congruent 2. 1 pair of opposite angles congruent 3. Diagonals perpendicular 4. Small diagonal bisected 5. Non-congruent angles are bisected 1. Opposite sides parallel. 2. Opposite sides congruent. 3. Opposite angles are congruent. 4. Consecutive angles are supplementary. 5. Diagonals bisect each other. 1. Has 4 right angles. 2. Diagonals are congruent. 3. All properties of parallelogram. 1. Has 4 Congruent sides 2. Diagonals bisect opposite angles. 3. Diagonals are perpendicular. 4. All properties of parallelograms. 1. 4 congruent sides and 4 congruent (right) angles 2. All properties of parallelogram, rectangle, and rhombus ACTIVITY

Quadrilateral Family:

Quadrilateral Family Shape is made up of 4 straight lines Square Trapezium Rectangle Rhombus Kite Parallelogram Quadrilateral

Quadrilateral Family:

Quadrilateral Family Shape is made up of 4 straight lines Square Trapezium Rectangle Rhombus Kite Parallelogram Quadrilateral

The Square:

(b) Opposite sides are parallel The Square (e) Turn symmetry (a) 4 sides are equal length (c) All angles are equal and are 90 o (d) It has 4 line of symmetry l l l l (f) Turn symmetry Properties of a square (g) If cut out it can fit back 8 different ways (h) Two diagonals are the same length (i) Diagonals bisect each other at 90 o (j) Diagonals bisect corner angles

The Rectangle:

(b) Opposite sides are parallel The Rectangle (e) Turn symmetry (a) Opposite sides have equal length (c) All angles are equal and are 90 o (d) It has 2 line of symmetry b b l l Properties of a rectangle (f) If cut out it can fit back 4 different ways (g) Diagonals are the same length (h) Diagonals bisect each other

The Rhombus:

(b) Opposite sides are parallel The Rhombus (e) Turn symmetry (a) All sides have equal length (c) Opposite angles are equal (d) It has 2 line of symmetry l l l l Properties of a rhombus (f) If cut out it can fit back 4 different ways (g) Diagonals bisect each other at 90 o (h) Diagonals bisect corner angles

The Kite:

(b) Left and right angles are the same The Kite (a) 2 pairs of adjacent sides of equal length (c) It has 1 line of symmetry C A l 1 l 1 Properties of a kite (d) If cut out it can fit back 2 different ways (e) Only one diagonal bisects the other (f) Diagonals cross each other at 90 o (g) One diagonal bisect corner angles B D l 2 l 2

The Parallelogram:

(b) Opposite pairs of sides are parallel The Parallelogram (d) Turn symmetry (a) Opposite pairs of sides have equal length (c) Opposite pairs of angles are equal (e) It has NO lines of symmetry C B Properties of a parallelogram (f) If cut out it can fit back 2 different ways (g) Diagonals bisect each other A D l 1 l 1 l 2 l 2

The Trapezium:

The Trapezium Has ONLY ONE property which is 1 pair of parallel lines Properties of a trapezium

Angles in a Quadrilateral:

Angles in a Quadrilateral IMPORTANT : The angles in a quadrilateral ALWAYS add up to 360 o C D A B We have split the quadrilateral into two triangles But for any triangle the sum of the angles is 180 0 Hence for the quadrilateral we have 2x180 o =360 o a o c o b o d o

Angles in a Quadrilateral:

Angles in a Quadrilateral Question : Find the missing angle below. x y z w 34 o 100 o The four angles of a quadrilateral add to = 360 o y o

Theorems about parallelograms:

Theorems about parallelograms 6.3—If a quadrilateral is a parallelogram, then its opposite angles are congruent. P ≅ R and Q ≅ S P Q R S

Theorems about parallelograms:

Theorems about parallelograms 6.4—If a quadrilateral is a parallelogram, then its consecutive angles are supplementary (add up to 180 °). m P +mQ = 180°, mQ +mR = 180°, mR + mS = 180°, mS + mP = 180° P Q R S

Theorems about parallelograms:

Theorems about parallelograms 6.5—If a quadrilateral is a parallelogram, then its diagonals bisect each other. QM ≅ SM and PM ≅ RM P Q R S

Polygons: Names, Definitions:

Polygons: Names, Definitions Parallelogram Square Rectangle Rhombus Trapezoid

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