leq: how do we classify and use properties of quadrilaterals?
TRANSCRIPT
![Page 1: LEQ: How do we classify and use properties of quadrilaterals?](https://reader038.vdocuments.us/reader038/viewer/2022102606/56649e4e5503460f94b458b0/html5/thumbnails/1.jpg)
Warmup: True or false: all rhombi are squares. Once warmup is completed, grab a note sheet and copy chart.
![Page 2: LEQ: How do we classify and use properties of quadrilaterals?](https://reader038.vdocuments.us/reader038/viewer/2022102606/56649e4e5503460f94b458b0/html5/thumbnails/2.jpg)
Chapter 6.1: Classifying
QuadrilateralsLEQ: How do we classify and use properties
of quadrilaterals?
![Page 3: LEQ: How do we classify and use properties of quadrilaterals?](https://reader038.vdocuments.us/reader038/viewer/2022102606/56649e4e5503460f94b458b0/html5/thumbnails/3.jpg)
A quadrilateral is a 4-sided polygon.
Box #1: “Quadrilateral”
![Page 4: LEQ: How do we classify and use properties of quadrilaterals?](https://reader038.vdocuments.us/reader038/viewer/2022102606/56649e4e5503460f94b458b0/html5/thumbnails/4.jpg)
“a quadrilateral with 2 pairs of congruent adjacent sides and no congruent opposite sides.”
No parallel sides
Box #2: “Kite”
![Page 5: LEQ: How do we classify and use properties of quadrilaterals?](https://reader038.vdocuments.us/reader038/viewer/2022102606/56649e4e5503460f94b458b0/html5/thumbnails/5.jpg)
“a quadrilateral with exactly one pair of parallel sides.”
Box #4: “Isosceles trapezoid”◦ Trapezoid who’s nonparallel opposite sides are
congruent.
Box #3: “Trapezoid”
![Page 6: LEQ: How do we classify and use properties of quadrilaterals?](https://reader038.vdocuments.us/reader038/viewer/2022102606/56649e4e5503460f94b458b0/html5/thumbnails/6.jpg)
“a quadrilateral with exactly 2 pairs of opposite parallel sides.
Why would the definition of trapezoid say “exactly one” pair of parallel opposite sides?
Box #5: “Parallelogram”
![Page 7: LEQ: How do we classify and use properties of quadrilaterals?](https://reader038.vdocuments.us/reader038/viewer/2022102606/56649e4e5503460f94b458b0/html5/thumbnails/7.jpg)
A parallelogram with a right angle.
Book definition “4 right angles.” Why don’t we need to say all four angles are 90 degrees?
Box #6: “Rectangle”
![Page 8: LEQ: How do we classify and use properties of quadrilaterals?](https://reader038.vdocuments.us/reader038/viewer/2022102606/56649e4e5503460f94b458b0/html5/thumbnails/8.jpg)
A parallelogram with 4 congruent sides.
Box #7: “Rhombus”
![Page 9: LEQ: How do we classify and use properties of quadrilaterals?](https://reader038.vdocuments.us/reader038/viewer/2022102606/56649e4e5503460f94b458b0/html5/thumbnails/9.jpg)
A parallelogram with 4 congruent sides and a right angle.
Book defn. “4 right angles”
Box #8: Square
![Page 10: LEQ: How do we classify and use properties of quadrilaterals?](https://reader038.vdocuments.us/reader038/viewer/2022102606/56649e4e5503460f94b458b0/html5/thumbnails/10.jpg)
“most precise”-means “most specific” aka lowest possible place on the chart.
Ex. A.) What is the most specific name for the figure below? B.) list all names that apply
Keep in mind: you may have to use coordinate plane to identify most precise name.
“most precise” vs. “all names that apply”
![Page 11: LEQ: How do we classify and use properties of quadrilaterals?](https://reader038.vdocuments.us/reader038/viewer/2022102606/56649e4e5503460f94b458b0/html5/thumbnails/11.jpg)
6.2 Properties of Parallelograms
LEQ: What are the properties of parallelograms?
![Page 12: LEQ: How do we classify and use properties of quadrilaterals?](https://reader038.vdocuments.us/reader038/viewer/2022102606/56649e4e5503460f94b458b0/html5/thumbnails/12.jpg)
3 Theorems Opposite sides are congruent Opposite angles are congruent The diagonals of a parallelogram bisect
each other
![Page 13: LEQ: How do we classify and use properties of quadrilaterals?](https://reader038.vdocuments.us/reader038/viewer/2022102606/56649e4e5503460f94b458b0/html5/thumbnails/13.jpg)
Thm. 6.1Why should the opposite sides of a
parallelogram be congruent?In the triangles below, prove AC=DB and AD=BCStatements Reasons
1.) m<1=m<2 1.) Alt. int. angles
3.) Reflexive3.) AB=AB
2.) “ “2.) m<3=m<4
4.)ABCBAD 4.) ASA
5.) AC=DB 5.) CPCTC
6.) “ “6.) AD=BC
1
D
C
B
A
4
3
2
![Page 14: LEQ: How do we classify and use properties of quadrilaterals?](https://reader038.vdocuments.us/reader038/viewer/2022102606/56649e4e5503460f94b458b0/html5/thumbnails/14.jpg)
Theorem 6-4
If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
![Page 15: LEQ: How do we classify and use properties of quadrilaterals?](https://reader038.vdocuments.us/reader038/viewer/2022102606/56649e4e5503460f94b458b0/html5/thumbnails/15.jpg)
Example
In the figure at the right, DH || CG, BF || AE, AB = BC = CD = 2 and EF = 2.5. Find EH.
A
FB
HD
E
GC