Download 1. What is the measure of one interior angle of a

September 17th
• Standard: MM1G3.d.: Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.
1. What is the measure of one interior angle of a
regular pentagon?
2. What is the measure of one exterior angle of
a regular pentagon?
3. What is a quadrilateral?
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Things to know:
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Investigation: What are some Properties of Kites?
Step 1: Draw 2 connected segments of different lengths, as shown. Fold through the segments and trace the two segments on the back of the patty paper.
Step 2: Compare the size of each opposite angles in your kite by folding an angle onto the opposite angle. Are the vertex angles congruent? Are the nonvertex angles congruent?
Kite angles conjecture ­ The __________Angles of a kite are______.
MM1G3.d.: Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.
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Step 3: Draw the Diagonals. How are they related?
Kite diagonals ­ The diagonals of a kite are ________
Step 4: Compare the lengths of the segments on both diagonals. Does either diagonal bisect the other?
Kite diagonals bisector ­ The diagonal connecting the vertex angles of a kite is the ________ of the other diagonal.
Step 5: Fold Along Both Diagonals. Does either diagonal bisect any angles?
Kite angle bisector ­ The ______angles of a kite are _____ by a ______. 4
Things to know about TRAPEZOIDS
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Investigation: What are some properties of trapezoids?
Step 1: Use the two edges of your straightedge to draw parallel segments of unequal length. Draw two non parallel sides connecting them to make a trapezoid.
Step 2: Use your protractor to find the sum of the measures of each pair of consecutive angles between the bases. Trapezoid consecutive angle conjecture ­ The consecutive angles between the bases of a trapezoid are ____________.
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Step 3: Using the isosceles trapezoid given to you, measure each pair of base angles.
Isosceles trapezoid conjecture ­ The base angles of an isosceles trapezoid are ___________
Draw both diagonals on your isosceles trapezoid. Compare their lengths.
Isosceles trapezoid diagonals conjecture ­ The diagonals of an isosceles trapezoid are __________
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Example problems:
1. Perimeter = _______
2. x = ______, y = ________
3. x = _____, y = _____
4. x = _____, perimeter = 85cm
5. x = _____, y = _____
6. x = ____, y = ___, perimeter = 164cm
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Properties of Midsegments
Definition of Midsegment: the segment connecting the midpoints of the two nonparallel sides of a trapazoid
Investigation: Triangle midsegment properties
Step 1: Draw a triangle on a piece of patty paper. Pinch the patty paper to locate the midpoint of all sides. Draw the midsegments.You should now have four small triangles.
Step 2: Using another piece of patty paper over the first, trace one of the smaller triangles.
Step 3: Compare all four triangles by sliding the copy of the smaller trianlge over the other three triangles.
Three midsegments conjecture ­ The three midsegments of a triangle divide it into _________________
Step 4: Compare the length of the midsegment to the large triangle's third side.
Triangle midsegment conjecture ­ A midsegment of a triangle is _______the length of the ________
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Investigation: Trapezoid Midsegment Properties
Step 1: Draw a small trapezoid on the left side of a piece of patty paper. Pinch the paper to locate the midpoints of the non parallel sides. Draw the midsegment.
Step 2: Label the angles as shown. Using a second sheet of patty paper over the first, copy the trapezoid and it's midsegment.
Step 3: Compare the trapezoids base angles with the corresponding angles at the midsegment by sliding the copy up over the original.
Step 4: Are the corresponding angles congruent? ______What can you conclude about the midsegment and bases? _________________________
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Let's investigate how the midsegment of a trapezoid compares to the length of the two bases? Using your two patty papers with trapezoids
Step 1: On the original trapezoid, extend the longer base to the right by atleast the length of the shorter base.
Step 2: Slide the second patty paper under the first. Show the sum of the lengths of the two bases by marking a point on the extension of the longer base. How many times does the midsegment fit onto the segment representing the sum of the length of the two bases?
The midsegment of a trapezoid is _______ to the bases and is equal in length to _______________________.
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Try these: 1. What is the perimeter of ? TOP
2. x = ____, y = ____
3. z = ________
5. What is the perimeter of TEN?
6. m = ___, n = ___, p = ___
7. q = _____
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Properties of Parallelograms
Investigation: Four Parallelogram Properties
Step 1: Using lines on a piece of graph paper as a quide, draw a pair of parallel lines that are atleast 6 cm apart. Using the parallel edges of your straightedge, make a parallelogram. Label it LOVE
Step 2: Measure the angles of the parallelogram LOVE. Compare a pair of opposite angles.
Parallelogram Opposite Angles Conjecture ­ The opposite angles of a parallelogram are _________
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Two angles that share a common side in a polygon are called consecutive angles. Step 3: Find the sum of the measures of each pair of consecutive angles in a parallelogram.
Parallelogram Consecutive Angle Conjecture ­ The consecutive angles in a parallelogram are _____.
Step 4: Look at the opposite angles of your parallelogram.
Parallelogram Opposite Sides Conjecture ­ The opposite sides of a parallelogram are _________
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Parallelogram Diagonals
Construct diagonals LV and OE, label the point they intersect point M.
Measure LM and VM. What can you conclude about point M? Parallelogram Diagonals Conjecture ­ The diagonals of a parallelogram ________
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Try These:
1. c = ____, d = ____
4. VF= 36m, EF = 24m,
EI = 42, what is the perimeter of NVI?
2. a = ____, b = ____
3. g = ____, h = ____
5. What is the perimeter?
6. e = ____, f = ____
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Rhombus
A 4­sided shape with all sides have equal length, and opposite sides are parallel and opposite angles are equal.
On your RHOMBUS, draw the diagonals with a straightedge. Use the corner of a piece of patty paper. What do you notice?
Rhombus Diagonal Conjecture: The diagonals of a rhombus are ______________
The diagonals and the sides of a rhombus form two angles at each vertex. Fold your patty paper to compare each pair of angles. The ______________ of a rhombus _________the angles of a rhombus.
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Do Rectangles diagonals have special Properties?
Using your grid paper, draw a large rectangle. Draw in both diagonals. With your ruler, compare the lengths of the two diagonals.
Recall that a rectangle is also a paralellogram, so it's diagonals also have the properties of a parallelogram. Rectangle Diagonal Conjecture: The diagonals of a rectangle are _______ and bisect each other. 24
A SQUARE is an equiangular rhombus
or
A SQUARE is an equilateral rectangle
A square is a parallelogram, a rectangle, and a rhombus. Use what you know about these properties of the three quadrilaterals to complete the following conjecture:
The diagonals of a square are ___________________, _________________ and bisect each other.
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Try These:
1. WREK is a rectangle
CR = 10, WE = _____
2. PARL is a parallelogram
y = _________
3. SQRE is a square
x = ______, y = ____
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Kite: http://www.mathsisfun.com/definitions/kite.html
Trapezoid: http://www.mathsisfun.com/definitions/trapezoid.html
Parallelogram: http://www.mathsisfun.com/definitions/parallelogram.html
Rhombus: http://www.mathsisfun.com/definitions/rhombus.html
Rectangle: http://www.mathsisfun.com/definitions/rectangle.html
Square: http://www.mathsisfun.com/definitions/square.html
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