quadrilaterals
DESCRIPTION
Quadrilaterals. Bryce Hall 4 Wennersten. Parallelograms. Definition: a quadrilateral having both pairs of opposite sides parallel to each other . Properties. The opposite sides are parallel The opposite sides are also congruent The opposite angles are congruent - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Quadrilaterals](https://reader035.vdocuments.us/reader035/viewer/2022081604/568164da550346895dd72c52/html5/thumbnails/1.jpg)
Quadrilaterals
Bryce Hall4 Wennersten
![Page 2: Quadrilaterals](https://reader035.vdocuments.us/reader035/viewer/2022081604/568164da550346895dd72c52/html5/thumbnails/2.jpg)
ParallelogramsDefinition: a quadrilateral having both pairs of opposite sides parallel to each other.
![Page 3: Quadrilaterals](https://reader035.vdocuments.us/reader035/viewer/2022081604/568164da550346895dd72c52/html5/thumbnails/3.jpg)
Properties• The opposite sides are parallel• The opposite sides are also
congruent• The opposite angles are congruent• The diagonals bisect each other
Bisects
![Page 4: Quadrilaterals](https://reader035.vdocuments.us/reader035/viewer/2022081604/568164da550346895dd72c52/html5/thumbnails/4.jpg)
Formulas for Parallelograms• Perimeter = 2a + 2b• Area = b x h– The area is b x h because a
parallelogram is basically just two right triangles and a rectangle, so the area = length x width and length x width = b x h :3
![Page 5: Quadrilaterals](https://reader035.vdocuments.us/reader035/viewer/2022081604/568164da550346895dd72c52/html5/thumbnails/5.jpg)
Properties we don’t Know
• The adjacents sides are parallel, so their measure is 180°
x + y = 180°
![Page 6: Quadrilaterals](https://reader035.vdocuments.us/reader035/viewer/2022081604/568164da550346895dd72c52/html5/thumbnails/6.jpg)
Rhombus• Definition: an equilateral
parallelogram, including the square as a special case.
![Page 7: Quadrilaterals](https://reader035.vdocuments.us/reader035/viewer/2022081604/568164da550346895dd72c52/html5/thumbnails/7.jpg)
Properties of Rhombuses• Have 4 equal/congruent/same sides• Their diagonals are perpendicular– Diagonals make right triangles
• The diagonals bisect their angles
![Page 8: Quadrilaterals](https://reader035.vdocuments.us/reader035/viewer/2022081604/568164da550346895dd72c52/html5/thumbnails/8.jpg)
Formulas• Perimeter = all four sides added
together– x + x + x +x (x4) = perimeter
• Area = length of 2 diagonals times ½– Area = ½ab
![Page 9: Quadrilaterals](https://reader035.vdocuments.us/reader035/viewer/2022081604/568164da550346895dd72c52/html5/thumbnails/9.jpg)
Properties of the Angles of a Rhombus(Stuff we don’t know yet)
• Adjacent sides of Rhombus are supplementary (Add up to 180°)
![Page 10: Quadrilaterals](https://reader035.vdocuments.us/reader035/viewer/2022081604/568164da550346895dd72c52/html5/thumbnails/10.jpg)
RectanglesDefinition: a parallelogram having four right angles.
gay rectangle
![Page 11: Quadrilaterals](https://reader035.vdocuments.us/reader035/viewer/2022081604/568164da550346895dd72c52/html5/thumbnails/11.jpg)
Properties of Rectangles• Four right angles (all 90°)• Diagonals are congruent
This picture is a rectangle!!!
![Page 12: Quadrilaterals](https://reader035.vdocuments.us/reader035/viewer/2022081604/568164da550346895dd72c52/html5/thumbnails/12.jpg)
Formulas of Rectangles• Perimeter is the two lengths and the
two heights added together– l + l + w + w = perimeter
• Area is the length times the width– l x w = height
![Page 13: Quadrilaterals](https://reader035.vdocuments.us/reader035/viewer/2022081604/568164da550346895dd72c52/html5/thumbnails/13.jpg)
Special Quadrilaterals!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!
![Page 14: Quadrilaterals](https://reader035.vdocuments.us/reader035/viewer/2022081604/568164da550346895dd72c52/html5/thumbnails/14.jpg)
Trapezoids• Definition: a quadrilateral plane figure
having two parallel and two nonparallel sides
![Page 15: Quadrilaterals](https://reader035.vdocuments.us/reader035/viewer/2022081604/568164da550346895dd72c52/html5/thumbnails/15.jpg)
Properties of Trapezoids• Only have one set of parallel sides• The midsegment is the average of the base
lengths• The midsegment is parallel to the bases• The angles on either side of the base are parallel• The diagonals are congruent• The adjacent angles are parallel (Add up to 180°)
b = base, a = leg
![Page 16: Quadrilaterals](https://reader035.vdocuments.us/reader035/viewer/2022081604/568164da550346895dd72c52/html5/thumbnails/16.jpg)
Formulas of Trapezoids• Perimeter is the length of every side– leg1 + leg2 + base1 + base2 =
perimeter• Area is the ½ of the height times
both of the bases added together– Area = ½ h (b + b)
![Page 17: Quadrilaterals](https://reader035.vdocuments.us/reader035/viewer/2022081604/568164da550346895dd72c52/html5/thumbnails/17.jpg)
Why we use the formula ½ h (b + b) for area of a Trapezoid
• The formula is based on two identical trapezoids side by side, so they’re a parallelogram!!!!
• We have to use the formula for parallelograms ( base x height)
• Since the are of this figurative parallelogram is two of the trapezoids, we find ½ of it!!!!!!!!
![Page 18: Quadrilaterals](https://reader035.vdocuments.us/reader035/viewer/2022081604/568164da550346895dd72c52/html5/thumbnails/18.jpg)
Kites• There’s no definition, but it looks like a
kite!
Gay kite!
![Page 19: Quadrilaterals](https://reader035.vdocuments.us/reader035/viewer/2022081604/568164da550346895dd72c52/html5/thumbnails/19.jpg)
Properties of a Kite• Two pairs of congruent sides• Two of the sides aren’t congruent• The diagonals are perpendicular• One pair of the opposite angles are congruent• The intersection of the diagonals make right
triangles (Because they’re perpendicular)• The long diagonal bisects the short one
![Page 20: Quadrilaterals](https://reader035.vdocuments.us/reader035/viewer/2022081604/568164da550346895dd72c52/html5/thumbnails/20.jpg)
Formulas for Kites• The perimeter is all of the sides added– a + a + b + b = perimeter
• Add the two diagonals and divide by 2 or multiply by ½– area = ½ ab
![Page 21: Quadrilaterals](https://reader035.vdocuments.us/reader035/viewer/2022081604/568164da550346895dd72c52/html5/thumbnails/21.jpg)
Isosceles trapezoids• There’s no definition, but an
isosceles trapezoid has one pair of equal sides!!!!!!!
(Isosceles trapezoids have the same formulas as normal trapezoids!)
![Page 22: Quadrilaterals](https://reader035.vdocuments.us/reader035/viewer/2022081604/568164da550346895dd72c52/html5/thumbnails/22.jpg)
Properties of Isosceles Trapezoids
• Pairs of the base angles are congruent
• Diagonals are congruent• The angles on either side of the
bases are the same size