Download Unit 5 Notes Packet Polygons

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Geometry/Trigonometry
Unit 5: Polygon Notes
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Date:
Period:
(1) Page 270 – 271 #8 – 14 Even, #15 – 20, #27 - 32
(2) Page 276 1 – 10, #11 – 25 Odd
(3) Page 276 – 277 #12 – 30 Even
(4) Page 283 #1- 14 All
(5) Page 283 – 284 #15 – 24; FF #32, 34
(6) Page 290 #1- 10
(7) Page 290 #11 – 26, Page 292 #39 - 42
(8) Page 296 #1 - 16
(9) Page 296 – 297 #17 – 24, #34, 36 and 38
(10) Page 302 #1 - 14
(11) Page 302 – 303 #15 - 26
(12) Page 309 #1 - 12
(13) Page 309 – 310 #13 – 22, 27, 28, 31 - 34
(14) Page 317 Chapter 6 Test
Geometry Notes 6.1 Exploring Polygons
Polygon – is formed by _______________________________ called ___________such that the
following are true:
Each side intersects with _________________________________, once at each _____________.
_______________________ with a common endpoint are ________________________.
_______________ – if no line that contains a side of the polygon contains a point in
__________________ of the polygon.
________________________ – one that is not convex.
They are classified by the ______________________ that they have.
Every polygon has vertices, an interior, interior angles, an exterior, exterior
angles, a perimeter and an area.
This is polygon ____________
or polygon ______________
or polygon ______________ or…
Diagonal – a segment that _____________________________________ vertices.
Equilateral – ____________ of the _____________ are _____________
Equiangular – ___________ of the _____________ are _____________
____________________ – both equilateral and equiangular
Geometry Notes 6.2 Angles of Polygons
Theorem 6.1 Polygon Interior Angles Theorem: The sum of the measures of the interior angles of a
convex n-gon is
Corollary to Theorem 6.1: The measure of each interior angle of a regular n-gon is
Theorem 6.2 Polygon Exterior Angles Theorem: The sum of the measures of the exterior angles, one
from each vertex, of a convex polygon is
Corollary to Theorem 6.2: The measure of each exterior angle of a regular n-gon is
To find the number of sides of a regular polygon, and are given…
(a) The measure of each interior angle…
(1)
Find an ____________________
(2)
_____________ that number into ________________
(Ex1)
If each interior angle is 135 degrees, how many sides does the regular polygon have?
Solution:
180 – 135 = 45
360/45 = 8…therefore it is an 8 sided figure
(b) The measure of each exterior angle
(1)
_____________ that number into ________________
(Ex2)
If each exterior angle is 30 degrees how many sides does the regular polygon have ?
Solution:
360/30 = 12…therefore it is a 12 sided figure
To find the measure of each exterior angle in a regular polygon, and are given…
(a) The number of sides…
(1)
_____________ that number into ________________
(Ex3)
Find the measure of each exterior angle in a regular polygon if it has 20 sides.
Solution:
360/20 = 18…therefore each exterior angle is 18 degrees
To find the measure of each interior angle in a regular polygon, and are given…
(a) The number of sides
(1)
_____________ that number into ________________
(2)
_____________that answer from ________________
(Ex4)
(P1)
Find the measure of each interior angle in a regular polygon if it has 15 sides.
Solution:
360/15 = 24 so each exterior angle is 24 degrees
180 – 24 = 156, so each interior angle is 156 degrees
You are given the measure of each interior angle in a regular polygon. How many sides does the
polygon have?
(a)
(b)
(c)
(P2)
You are given the measure of each exterior angle in a regular polygon. How many sides does
the polygon have?
(a)
(b)
(c)
(P3)
You are given the number of sides in a regular polygon. Find the measure of each exterior angle
of the polygon.
(a)
10
(b)
20
(c)
36
(P4)
You are given the number of sides in a regular polygon. Find the measure of each interior angle
of the polygon.
(a)
8
(b)
12
(c)
14
Geometry Notes 6.3 Properties of Parallelograms
Special Quadrilaterals
Parallelogram – a ______________________ whose __________________ are______________.
Properties of Parallelograms
Theorem 6.3: If a quadrilateral is a parallelogram, then its opposite sides are congruent.
Theorem 6.4: If a quadrilateral is a parallelogram, then its opposite angles are congruent.
Theorem 6.5: If a quadrilateral is a parallelogram, then its consecutive angles are
supplementary.
Theorem 6.6 Diagonals of a Parallelogram: If a quadrilateral is a parallelogram, then the
diagonals bisect each other.
Geometry Notes 6.4 Proving Quadrilaterals are Parallelograms
Ways to prove ________________ are ___________________________
Theorem 6.7: If both pairs of opposite sides of a quadrilateral are congruent, then the
quadrilateral is a parallelogram.
Theorem 6.8: If both pairs of opposite angles of a quadrilateral are congruent, then the
quadrilateral is a parallelogram.
Theorem 6.9: If an angle of a quadrilateral is supplementary to both consecutive angles then the
quadrilateral is a parallelogram.
Theorem 6.10: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a
parallelogram.
Theorem 6.11: If one pair of opposite sides of a quadrilateral are congruent and parallel, then
the quadrilateral is a parallelogram.
Geometry Notes 6.5 Special Parallelograms
Rhombus – a ___________ with that has all ____________________
Rectangle – a _____________ that has ________________________
Square – a ____________ that is ___________________________
Theorem 6.12: A parallelogram is a rhombus if and only if its diagonals are perpendicular.
Theorem 6.13: A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite
angles.
Theorem 6.14: A parallelogram is a rectangle if and only if its diagonals are congruent.
Theorem 6.15: A quadrilateral is a rhombus if and only if it has four congruent sides.
Theorem 6.16: A quadrilateral is a rectangle if and only if it has four right angles.
Geometry Notes 6.6 Trapezoids
Trapezoid
(a)
________________ of opposite ___________ sides
(b)
The ____________________ are called the _______
(c)
The _________________ sides are called the _____
(d)
__________________ if the _____are ___________
(e)
______________ – there are ____________
(f)
_____________– connects the midpoints of its legs
Base Angles
Theorem 6.17 Trapezoid Base Angles Theorem: If a trapezoid is isosceles, then each pair of base
angles are congruent.
Theorem 6.18 Trapezoid Diagonals Theorem: If a trapezoid is isosceles, then its diagonals are
congruent.
Theorem 6.19: If a trapezoid has one pair of congruent base angles, then it is an isosceles
trapezoid.
Theorem 6.20: If a trapezoid has congruent diagonals, then it is an isosceles trapezoid.
Theorem 6.21 Midsegment Theorem for Trapezoids: The midsegment of a trapezoid is parallel
to each base, and its length is half the sum of the bases.
Geometry Notes 6.7 Congruence and Kites (Optional)
Two ______________________ are ________________ if their ___________________ and
_____________________ are ____________________________.
Theorem 6.22 __________________ Congruence Theorem: If three sides and the included
angles of one quadrilateral are congruent to the corresponding three sides and included angles
of another quadrilateral, then the quadrilaterals are congruent.
Theorem 6.23 ___________________Congruence Theorem: If three angles and the included
sides of one quadrilateral are congruent to the corresponding three angles and included sides of
another quadrilateral, then the quadrilaterals are congruent.
Kite
(a)
Two pairs of ___________________________________________, but opposite sides
are ________________________________
Theorem 6.24: If a quadrilateral is a kite, then its diagonals are perpendicular.
Theorem 6.25: If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.