MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C904F0.3D3ED580" This document is a Single File Web Page, also known as a Web Archive file. If you are seeing this message, your browser or editor doesn't support Web Archive files. Please download a browser that supports Web Archive, such as Microsoft Internet Explorer. ------=_NextPart_01C904F0.3D3ED580 Content-Location: file:///C:/45195D13/chapter_9_skeleton_notes.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Chapter 9: Geometry

Topics in Mathematics

Chapter 9 Homework Assignments=

 

 

Section 9.1 = ;         3-11, 45-70, 71, 73, 75, 77, 79, 81, 83, 85

 

Section 9.2 = ;         1, 2, 3, 5, 6, 15-34, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53-68

 

Section 9.3 = ;         1-4, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 55

 

Section 9.4 = ;         7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 41, 43, 45<= /o:p>

 

Chapter 9:  Geometry

 

Section 9.1:&nb= sp; Points, Lines, Planes, and Angles

 

Eucl= idean Geometry (Plane Geometry):  Two-dimensional geometry (Euclid was a great mathematician who wrote The Elements)

&nbs= p;

Unde= fined Terms:  The building blocks of geometry.  These ter= ms are understood by their relationship to the every-day world.

&nbs= p;

Defi= nitions:  Used to describe elements of geometry.  Often based on unde= fined terms.

&nbs= p;

Axio= ms (Postulates):  Propositions that must be accepted as true without proof.

&nbs= p;

Theo= rems:  Propositions that are proved using axioms and reason.

&nbs= p;

Poin= t:

 

&nbs= p;

&nbs= p;

Line= :

 

 

 

 

&nbs= p;

&nbs= p;

&nbs= p;

&nbs= p;

Description

Di= agram

Sy= mbol

 

 

 

 

 

 

 

 

 

&nbs= p;

&nbs= p;

Plan= e:

 

 

 

 

 

&nbs= p;

&nbs= p;

&nbs= p;

Para= llel Lines:

 

&nbs= p;

&nbs= p;

Skew= ed Lines:

 

&nbs= p;

&nbs= p;

Angl= e:

 

 

 

&nbs= p;

&nbs= p;

&nbs= p;

Vert= ex:

 

&nbs= p;

&nbs= p;

Meas= ure of an Angle:

 

 

&nbs= p;

&nbs= p;

Degr= ee:

 

 

&nbs= p;

&nbs= p;

Righ= t Angle:

 

&nbs= p;

&nbs= p;

Acut= e Angle:

 

&nbs= p;

&nbs= p;

Obtu= se Angle:

 

&nbs= p;

&nbs= p;

Stra= ight Angle:

 

&nbs= p;

&nbs= p;

Adja= cent Angles:

 

Comp= lementary Angles:

 

&nbs= p;

&nbs= p;

Supp= lementary Angles:

 

&nbs= p;

&nbs= p;

Exam= ples:

&nbs= p;

 


D
 

C
 

B
 
        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p; m    CBD =3D 27°

 

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p; Find m    ABC

 

 

 

 

 

 


        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p; Find m    ABC        &= nbsp;     Find m    CBD

 

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;

 

 

 

 

 

 

    EFG and     GFH are supplemen= tary angles.  m    EFG is 5 times m    GFH.  Find the measure of both angles.

 

 

 

 

 

 

 

 

 

    XYZ and     WYX are complementary angles.  m    XYZ is 17 ° greater than<= /p>

        &= nbsp;   m    WYX.  Find the measure of both angles.

 

 

 

 

 

 

 

 

Vert= ical Angles:

 

 

 

 

 

Tran= sversal:

 

 

 

T= wo Lines Cut by a Transversal

 

 

 

 

 

 

 

 

 

 

 

Inte= rior Angles

 

 

 

Exte= rior Angles.

 

 

 

Alte= rnate Interior Angles:

 

 

 

Alte= rnate Exterior Angles:

 

 

 

Corr= esponding Angles:

 

 

 

 

When= Two Parallel Lines are Cut by a Transversal:

 

 

 

 

 

 

Exam= ples:

 

 

 

 

 

 

 

 

 

 

 


m    1 =3D 112°.  Find all other angles.

 

 

 

 

 

 

 

 

 

 

 

 

 

Sect= ion 9.2:  Polygons

 

Poly= gon:

 

 

 

Side= s:

 

 

 

Vert= ex:

 

 

 

Regu= lar Polygon:

 

 

 

Number of Sides

Name

Sum of Angles

3

 

 

4

 

 

5

 

 

6

 

 

7

 

 

8

 

 

 

 

Theo= rem:  The sum of the interior angles of a triangle is 180°.

 


Proo= f:

 <= /o:p>

 

 

 

 

 

 

 

 

 

 



Sum = of the Interior Angles of a Quadrilateral:

 

 

 

 

 

Sum = of the Interior Angles of a Pentagon:

 

 

 

 

 

Sum = of the Interior Angles of a Polygon:

 

 

Exam= ples:

 

Find the sum of the interior angles of a hexagon.

 

 

 

Find the measure of each interior angle of a regular hexagon.

 

 

 

Find the sum of the interior angles of an octagon.

 

 

 

Find the measure of each interior angle of a regular octagon.

 

 

 

Find the sum of the interior angles of a ten-sided polygon.

 

 

 

Find the measure of each interior angle of a regular ten-sided polygon.

 

 

 

T= ypes of Triangles

Acute Triangle:

 

 

 

Obtu= se Triangle:

 

 

 

Right Triangle:

 

 

 

Isos= celes Triangle:

 

 

 

Equi= lateral Triangle:

 

 

 

Scal= ene Triangle:

 

 

 

Simi= lar Figures:

 

 

 

Corr= esponding Sides, Corresponding Angles:

 

 

 

 

Simi= lar Polygons:

 

 

 

Prop= ortion:

 

Exam= ples:

 

 

 

 

 

 

 

 


ΔABC is similar to ΔA’B’CR= 17;

B’
 
Find the lengths of A’B’ and B’C’.=

 

 

 

 

 

 =

 

 

 

 

 

 

 

A
 
 

 

 

 

 

 

 

 

 

 


ΔABC is similar to ΔEFG

Find the lengths of AC and FG.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cong= ruent Polygons:

 

 

 

 

T= ypes of Quadrilaterals

Trap= ezoid:

 

 

 

Para= llelogram:

 

 

 

Rect= angle:

 

 

 

Rhom= bus:

 

 

 

Squa= re:

 

 

 

 

 

 

Sect= ion 9.3:  Perimeter and Area

 

Peri= meter:

 

 

 

Exam= ple:

 

 

 

 

 

 

 

 

 


Area= :

 

 

 

Area Formulae

Fi= gure

Ar= ea

Rectangle

 

Square

 

Parallelogram

 

Triangle

 

Trapezoid

 

 

Pyth= agorean Theorem:

 

 

 

 

 

Exam= ples:

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;             =

    = ;            &n= bsp;            = ;            &n= bsp;            = ;            &n= bsp;            = ;    

20m
 
=             &nb= sp;            =             &nb= sp;            =             &nb= sp;            =          <= /p>

    = ;            &n= bsp;            = ;            &n= bsp;            = ;            &n= bsp;            = ;    

48m
 
    = ;            &n= bsp;            = ;            &n= bsp;            = ;            &n= bsp;            = ;    

 

6”
 
    &n= bsp;            = ;            &n= bsp;            = ;            &n= bsp;            = ;            &n= bsp;   

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;             =

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;             =

12”
 
    &n= bsp;            = ;            &n= bsp;            = ;            &n= bsp;            = ;            &n= bsp;   

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;             =

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;             =

 

 

 

 

Circ= le:

 

 

 

Radi= us:

 

 

 

Diam= eter:

 

 

 

Circ= umference:

 

 

 

Area= of a Circle:

 

 

 

Exam= ples:

 

Find the circumference and area of a circle with a radius of 8”.

 

 

 

 

 

 

 

Find the circumference and area of a circle with a diameter of 6cm.

 

 

 

 

 

 

 

 

Sect= ion 9.4:  Volume

 

Solid Geometry:

 

 

 

Volu= me:

 

 

 

Volu= me Formulae

Fi= gure

Vo= lume

Rectangular Solid

 

Cube

 

Cylinder

 

Cone

 

Sphere

 

 

Pris= m:

 

 

 

 

Righ= t Prism:

 

 

 

Volu= me of a Prism:

 

 

 

Pyra= mid:

 

 

 

Volu= me of a Pyramid:

 

 

 

 

 

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Geometry

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