Download Rubric: 15 possible points

Ch 6 QUADRILATERALS
Objectives:
Section 6-1
Section 6-2
Section 6-3
Section 6-4
Section 6-5
Section 6-6
Section 6-7
To define and classify special quadrilaterals
To use relationships between sides and angles of parallelograms
To use relationships involving diagonals of parallelograms or transversals.
To determine if a quadrilateral is a parallelogram.
To use properties of diagonals of rhombuses and rectangles.
To determine if a parallelogram is a rhombus or a rectangle.
To verify and use properties of kites and trapezoids
Use properties of special quadrilaterals to name coordinates.
To prove theorems using figures in a coordinate plane.
Theorems and Postulates:
T 6-1:
Opposite sides of a parallelogram are congruent.
T 6-2:
Opposite angles of a parallelogram are congruent.
T 6-3:
The diagonals of a parallelogram bisect each other.
T 6-4:
If three or more lines create congruent segments on a transversal, then they cut off
congruent segments on every transversal.
T 6-5:
Converse of T 6-3 If the diagonals of a quadrilateral bisect each other, then the
figure is a parallelogram.
T 6-6:
If one pair of opposite sides of a quadrilateral is both parallel and congruent, then the
figure is a parallelogram.
T 6-7:
Converse of T 6-1 If both pairs of opposite sides of a quadrilateral are congruent,
then the figure is a parallelogram.
T 6-8:
Converse of T 6-2 If both pairs of opposite angles of a quadrilateral are congruent,
then the figure is a parallelogram.
T 6-9:
Each diagonal of a rhombus bisects two angles of the rhombus.
T 6-10:
The diagonals of a rhombus are perpendicular.
T 6-11:
The diagonals of a rectangle are congruent.
T 6-12:
If one diagonal of a parallelogram bisects two angles of the parallelogram, then the
parallelogram is a rhombus.
T 6-13:
If the diagonals of a parallelogram are perpendicular, then the parallelogram is a
rhombus.
T 6-14:
If the diagonals of a parallelogram are congruent, then the parallelogram is a
rectangle.
T 6-15:
The base angles of an isosceles trapezoid are congruent.
T 6-16:
The diagonals of an isosceles trapezoid are congruent.
T 6-17:
The diagonals of a kite are perpendicular.
T 6-18:
a. The midsegment of a trapezoid is parallel to the bases.
b. The length of the midsegment of a trapezoid is half the sum of the lengths of the
bases.
Vocabulary:
parallelogram
square
isosceles trapezoid
rhombus
kite
consecutive angles
rectangle
trapezoid
Homework
Daily Work
4 HW pts
possible
each day
HW
REQUIRED Algebra Review: p 355: 1 – 23 odd Show your work, and use the
examples. Note the bulleted rules.
6.1: p 290-292: 7-12, 14, 15, 21, 22, 26, 30-32, 37-42, 46-49
6.2: p 297-299: 3-15 (x3), 34, 36, 37
6.2: p 297-301: 18, 20, 22, 39, 42, 51, 56, 58
6.3: p 307-310: 3-15 (x3), 21-25, 29, 30, 36 checkpoint quiz 1-10 (check answers in
back of book)
6.4: p 315-318: 3-15 (x3), 16 – 20 even, 23, 25-34, 45-47, 50, 54, 61
6.5: p 322-325: 2-6 even, 9-27 (x3), 34-36, 40, 41, 54-56
p 331: checkpoint quiz 1-8 (check answers in back of book)
6.6: p 328-331: 3 – 12 (x3), 29, 30, 32
Journal
Answer each of the following using complete sentences.
10 points
possible
1. Given: A quadrilateral with congruent diagonals. Explain when it is a rectangle, and when it
is not a rectangle. In your explanation, describe the relationship between the diagonals, not
the characteristics of the quadrilateral.
Due date:
2. Write two different biconditionals about parallelograms.
3. ABCD is a square. Using quadrilateral classifications we have learned, what else can a
square be called? Explain.
4. Angie says that if the diagonals of a quadrilateral are perpendicular, then the quadrilateral is
a kite or a rhombus. Provide a counterexample and an explanation to demonstrate why
Angie’s claim is false. Be sure to include a sketch.
Vocabulary
formulas
15 points
possible
Due date:
V-1. Make a mobile that demonstrates the quadrilateral hierarchy (see page 289).
You must include the definition and properties of each quadrilateral. Presentation
is important!
V-2 Complete the Quadrilateral Properties table *
Be prepared to take an oral quiz over the properties. You must answer 5
questions correctly for full credit.
V-3 Make a crossword puzzle for the chapter vocabulary with precise clues relating
to the definitions and properties of quadrilaterals. You must have at least 15 clues.
Please turn in the puzzle, and the solution. Presentation is important! See me if
you’d like cm grid paper to draw your crossword, or there are a number of
websites for making crosswords.
Level 2
2-1 (6.1)page 293: 56-59 Be sure to name ALL possible quadrilaterals. (2 pts each)
2-2 (6.1) Quadrilaterals in the real world. (1 pt each)
12 points
possible
Find examples of four different special quadrilaterals in the real world. You may
use print illustrations, photographs, or write descriptions. Consider architecture,
household products, advertising, or anything else you encounter. Justify each
classification by using measurements.
Due date:
2-3 (6.1) * Missing angle measures. (8 pts)
2-5 (6.3) * Inside Secrets of a Polygon (8 pts)
2-6 (6.5) Isosceles Trapezoid (8 pts)
Draw and label an isosceles trapezoid. Draw the diagonals. Write congruence
statements for all pairs of triangles you can prove are congruent.
2-7
(6.6) * Right Triangle Coordinate proof (8 pts)
Prove the following: The midpoint of the hypotenuse of a right triangle is
equidistant from the vertices of the triangle.
Level 3
15 points
possible
Due date:
3-1 (6.1) * Find the quadrilateral (15 pts)
3-2 (6.1) Make a box kite (Start early, this will take some time) Here are some web
sites that may help. (15 pts)
http://www.howtomakeandflykites.com/kites-to-make/the-box-kite.html
http://www.my-best-kite.com/how-to-make-a-box-kite.html
http://www.drachen.org/pdf/KonoBoxKite/DownloadInstructions.pdf
http://www.my-best-kite.com/building-box-kites.html -good tips!
3-3 (6-3) complete problem 37 on page 309 (8 pts)
3-4 (6.4) Rhombus Proof (8 pts)
Prove the following: If one diagonal of a parallelogram bisects one angle of a
parallelogram, then the parallelogram is a rhombus. (Note: this is similar to
Theorem 6-12, but only states one angle.)
3-5 (6.5) * Making Something Out of Nothing (8 pts)
Vocabulary
V-2
Quadrilateral Properties table
Complete the table below by placing a yes (to mean always) or a no (to mean not always) in each box.
Use what you know about special quadrilaterals.
Kite
Isosceles
Trapezoid
Parallelogram
Rhombus
Rectangle
Opposite Sides
are Parallel
Opposite Sides
are Congruent
Opposite Angles
are Congruent
Diagonals Bisect
Each Other
Diagonals are
Perpendicular
Diagonals are
Congruent
Exactly One Line
of Symmetry
Exactly Two
Lines of
Symmetry
After table is complete and correct, take an oral quiz to demonstrate your understanding.
Square
Level 2
2-2 (6.1) Quadrilaterals in the Real World
Find examples of four different special quadrilaterals in the real world. You may use print
illustrations, photographs, or write descriptions. Consider architecture, household products,
advertising, or anything else you encounter. Justify each classification by using measurements
(either listed with the image, or through you using measuring tools).
2-3 (6.1)
Missing Angle Measures
Using the diagram below, find the value of each lettered angle. Show all your calculations on
this page. Explain how you determined measures e, f, and g.
a _____
b _____
m _____
p _____
c ______
d _____
e ______
g _____
Explanation of e, f, and g values
____________________________________________________
____________________________________________________
____________________________________________________
____________________________________________________
____________________________________________________
____________________________________________________
________________________________________________
2-5 (6.3) Inside Secrets of a Polygon
2-7 (6.6) Right Triangle Coordinate proof
Complete the following steps to prove that the midpoint of the hypotenuse of a right triangle is
equidistant from the vertices of the triangle. Show all your work on a separate page. Turn in all
your calculations, and your coordinate grid.
Given: Right triangle ABC with M the midpoint of the hypotenuse of AB .
Prove: MA  MB  MC
1. Draw right triangle ABC on a coordinate plane. Place the right angle, C, at the origin, and A on
the positive x-axis.
2. Label the coordinates using variables. Since you are working with midpoints, it is best to use
multiples of 2, for example (2a, 2b).
3. Use the midpoint formula to find the coordinates of M the midpoint of AB .
4. Use the distance formula to find MA, MB, and MC.
5. What conclusion can you draw?
Level 3
3-1 (6.1) Find the Quadrilateral
The paper for Part One is provided; use notebook paper for Parts 2-5 and clearly label each section, and
attach this rubric to your project.
Rubric: 15 possible points
Possible
points
Self
points
Actual
points
Comments
PART ONE (use provided Part)
Pick 4 points on the coordinate grid using the
guidelines on the following page
.5
Name each point (x, y) location and graph
Label the 4 points A, B, C and D
.2
Draw all 4 segments AB, BC, CD, and AD
.1
* make sure ABCD is a quadrilateral
PART TWO
Find the midpoint of segment AB (show work)
1
Find the midpoint of segment BC (show work)
1
Find the midpoint of segment CD (show work)
1
Find the midpoint of segment AD (show work)
1
Name each midpoint (x, y) location and graph
.1
Label the 4 midpoints E, F, G and H
.1
Inscribe a quadrilateral from the midpoints
1
PART THREE
* graph midpoints on Part One
* length in simplest radical form!
Find the length of segment EF (show work)
1
Find the length of segment FG (show work)
1
Find the length of segment GH (show work)
1
Find the length of segment EH (show work)
1
PART FOUR
* slope as an improper fraction!
Find the slope of segment EF (show work)
.1
Find the slope of segment FG (show work)
.1
Find the slope of segment GH (show work)
.1
Find the slope of segment EH (show work)
.1
Identify the inscribed quadrilateral
.5
PART FIVE
* equation in slope-intercept form!
Find the equation of segment EF (show work)
1
Find the equation of segment FG (show work)
1
Find the equation of segment GH (show work)
1
Find the equation of segment EH (show work)
1
Total
15
points
FIND THE QUADRILATERAL: PART ONE
Name: ________________________________________
Transform your facts into coordinate points.
Age: _____ Number of siblings (including yourself): _____
(Age, Siblings)
=(
,
)
Height: _____ feet and _____ inches
(Feet – 7, Inches)
=(
,
)
Num. of letters in your first name _____ and last name _____
(-1 x First, -1 x Last)
=(
,
)
Birthday: _____ / _____ / __________ (month/day/year)
(Month, Day – 15)
=(
,
)
3-5 (6.5) Making Something Out of Nothing
A square 8 units on each side is divided into 4 sections (two right triangles, and two trapezoids)
as shown in figure 1 below. Cut out and reassemble these shapes into the 13-by-5 rectangle in
figure 2.
Use the information in the diagrams above to answer the questions 1 – 3.
1. What is the area of the square?
2. What is the area of the rectangle?
3. Explain why these two differ.
Without cutting and reassembling, sketch the square that would appear to be the reconstruction
of the shapes of the given rectangle below. Label all measures.
4. By how much do the areas differ?