Geometry Chapter 6
Lesson 1 – Properties and Attributes of Polygons
Sides of a Polygon:
Vertex of a Polygon:
Diagonal:
Regular Polygon:
Concave:
Convex:
Note: Know the names of polygons found on page 382.
Polygon Angle Sum Theorem:
Polygon Exterior Angle Sum Theorem:
Examples:
1. Tell whether each figure is a.
a polygon. If it is, name it by
the number of sides.
b.
c.
2. Tell wether each polygon
is regular or irregular. Tell
whether it is concave or
convex.
a.
b.
c.
3a. Find the sum of the
interior angle measures of a
convex heptagon.
b. Find the measure of each
interior angle of a regular
16-gon.
c. Find the measure of
each interior angle of
pentagon ABCDE.
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4a. Find the sum of each
exterior angle of a regular
20-gon.
b. Find the value of b in polygon FGHJKL.
5. Ann is making paper stars
for party decorations. What is
the measure of ∠1?
Lesson 2 – Properties of Parallelograms
Parallelogram:
Properties of Parallelograms:
1.
2.
3.
4.
1. In CDEF, DE=74mm, DG=31mm, & m∠FCD=42o.
Find each measure.
a. CF
2. WXYZ is a parallelogram. Find each measure.
a. YZ
b. m∠Z
b. m∠EFC
c. DF
3. EFGH is a parallelogram.
a. Find GJ
4. Given: ABCD is a parallelogram
Prove: ∆AEB ≅ ∆CED
b. Find FH
1.
2.
3.
4.
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5. Three vertices of JKLM are J(3, -8); K(-2, 2); & L(2, 6).
Find the coordinate of vertex M.
Lesson 3 – Conditions for Parallelograms
Conditions for a Parallelogram:
1.
4.
2.
5.
3.
Examples:
1a. Show that JKLM is a parallelogram for a=3 & b=9.
b. Show that PQRS is a parallelogram for x=10 & y=6.5
2. Determine if each quadrilateral must be a parallelogram.
Justify your answer.
a.
b.
3. Show that quadrilateral JKLM is a parallelogram by using
the given definition or theorem.
a. J(-1, -6); K(-4, -1); L(4, 5); M(7, 0): def of parallelogram
b. A(2, 3); B(6, 2); C(5, 0); D(1, 1); 1pr opp sides // & ≅
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Lesson 4 – Properties of Special Parallelograms
Rectangle:
Properties of Rectangles:
1.
2.
Rhombus:
Properties of Rhombus:
1.
3.
2.
Square:
Examples
1. A woodworker constructs a rectangular picture frame so
that JK=50cm and JL=86cm. Find HM.
2. TVWX is a rhombus. Find each measure.
a. TV
b. m∠VTZ
3. Show that the diagonals of square EFGH are congruent perpendicular bisectors of each other.
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Lesson 5 – Conditions for Special Parallelograms
Conditions for a Rectangle
1.
2.
Conditions for a Rhombus
1.
3.
2.
Condition for a Square
1.
1. A manufacturer builds a mold for a desktop so that
2. Determine if the conclusion is valid. If not, tell what
AB ≅ CD, BC ≅ DA, & m∠ABC=90. Why must ABCD be additional information is needed to make it valid.
a. Given: EF ≅ FG, EG ⊥ FH
a rectangle?
Conclusion: EFGH is a rhombus
b. Given: EB ≅ BG, FB ≅ BH, EG ≅ FH,
∆EBF ≅∆EBH
Conclusion: EFGH is a square.
3. Use the diagonals to determine whether a parallelogram with the given vertices is a rectangle, rhombus, or square. Give
all the names that apply.
a. P(-1, 4); Q(2, 6);R(4, 3); S(1, 1)
b. W(0, 1); X(4, 2); Y(3, -2); Z(-1, -3)
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Lesson 6 – Properties of Kites and Trapezoids
Kite:
Properties of Kites
1.
2.
Trapezoid:
Base:
Legs:
Base Angles:
Isosceles Trapezoid:
Properties of Isosceles Trapezoids
1.
3.
2.
Trapezoid Midsegment Theorem:
1. Lucy is framing a kite with
wooden dowels. She uses two
dowels that measure 18cm, one
dowel that measures 30cm, and
two dowels that measures 27cm.
To complete the kite she needs a
dowel to place along KL. She
has a dowel that is 36cm. About
how much wood will she have
left over after cutting the last
dowel?
2. In kite ABCD, m∠DAB=54 &m∠CDF=52. Find each
measure.
3a. Find m∠A.
4a. Find the value of a so that PQRS is isosceles.
a. m∠BCD
b. m∠ABC
c. m∠FDA
b. KB=21.9 & MF=32.7, find FB
b. AD=12x – 11 & BC=9x – 2. Find the value of x
so that BCD is isosceles.
5a. Find EF
b. Find EH
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Chapter 6 – Polygons and Quadrilaterals
Homework Assignments
Lesson
Problems
6.1 p. 386
#16-31, 46-50, 53-55
6.2 p. 395
#1-14, 21-24, 41-43
6.3 p. 402
#9-14, 16-23, 26, 32, 35-37, 44-49
6.4 p. 412
#10-16, 18-31, 40-43, 45-47
6.5 p. 422
#6-17, 20-22, 24-27, 33, 39-41
6.6 p. 433
#14-22, 27, 29-31
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