PowerPoint Presentation: DEEPAK SHARMA KAPIL GYANPEETH MATHEMATICS
ACTIVITY: ACTIVITY The fold crease QUADRILATERALS Parallelogram
ACTIVITY: QUADRILATERALS ACTIVITY
PowerPoint Presentation: Parallelograms Now, Let’s review what we learned last class
PowerPoint Presentation: A quadrilateral is a PARALLELOGRAM if and only if it has two sets of parallel sides
PowerPoint Presentation: 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
PowerPoint Presentation: RECTANGLE A parallelogram with FOUR RIGHT ANGLES
PowerPoint Presentation: A quadrilateral is a RECTANGLE if and only if it has four right angles
PowerPoint Presentation: RECTANGLE Diagonals are Congruent
ACTIVITY: 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
PowerPoint Presentation: RHOMBUS A parallelogram with FOUR CONGRUENT SIDES
PowerPoint Presentation: A quadrilateral is a RHOMBUS if and only if it has four congruent sides
PowerPoint Presentation: RHOMBUS Diagonals Bisect A Pair of Opposite Angles
PowerPoint Presentation: Diagonals are Perpendicular RHOMBUS
ACTIVITY: 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
PowerPoint Presentation: A quadrilateral is a SQUARE if and only if it has four congruent sides and four right angles
PowerPoint Presentation: SQUARE A parallelogram with FOUR RIGHT ANGLES AND FOUR CONGRUENT SIDES
PowerPoint Presentation: Holds same properties as Rhombus and Rectangle SQUARE
ACTIVITY: 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
PowerPoint Presentation: Trapezoid ONE PAIR OF PARALLEL SIDES
PowerPoint Presentation: A quadrilateral is a TRAPEZOID if and only if it has ONE pair of parallel sides
PowerPoint Presentation: Trapezoid leg leg base base Leg angles are supplementary Leg angle 1 Leg angle 2
PowerPoint Presentation: Trapezoid Base (b 2 ) Base (b 1 ) Midsegment is ½ the sum of the lengths of the bases Midsegment =½ (b 1 + b 2 )
PowerPoint Presentation: Trapezoid leg leg base base Isosceles: Base angles are congruent Base angle 2 Base angle 1
PowerPoint Presentation: Trapezoid Isosceles: Diagonals are congruent
PowerPoint Presentation: KITE TWO PAIRS OF CONSECUTIVE CONGRUENT SIDES (opposite sides not congruent)
PowerPoint Presentation: A quadrilateral is a KITE if and only if it has two pairs of congruent consecutive sides
PowerPoint Presentation: KITE Diagonals are perpendicular
PowerPoint Presentation: KITE Short diagonal is bisected
PowerPoint Presentation: KITE ONE pair of opposite angles are congruent (not both)
PowerPoint Presentation: KITE The other angles are bisected by the diagonal
ACTIVITY: 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 +mQ = 180°, mQ +mR = 180°, mR + mS = 180°, mS + mP = 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