Chapter 13
Math 366 Chapter 13 Review Problems
1. Complete the following.
a. 45 ft = _ yd
e. 7 km = _ m
b. 947 yd = _ mi
f. 173 cm = _ m
c. 0.25 mi = _ ft
g. 67 cm = _ mm
d. 289 in. = _ yd
h. 132 m = _ km
2. Given three segments of length p, q, and r, whe
Section 12-1
Math 366 Lecture Notes
Section 12.1 Congruence Through Constructions
Similar objects have the same shape but not necessarily the same size.
Notation: ABC DEF
Congruent objects have the same shape and same size.
Notation: ABC DEF
Are similar o
Section 12-2
Math 366 Lecture Notes
Section 12.2 Other Congruence Properties
Theorem 12-6
Angle, Side, Angle (ASA)
If two angles and the included side of one triangle are congruent to two angles and the included
side of another triangle, respectively then
Section 12-3
Math 366 Lecture Notes
Section 12.3 Other Constructions
A rhombus is a parallelogram in which all the sides are congruent.
Properties of a Rhombus:
1. A quadrilateral in which all the sides are congruent is a rhombus.
2. Each diagonal of a rh
Section 11.2
The distance from A to B= length of AB d(A,B) = AB
d(A,B) = d(B,A)
Triangle inequality AC + CB > AB
Perimeter =circumference
Circumference/diameter related by pi
Sector= slice of pie
*Perimeter of sector= 20+ 5pi/2
Greatest possible error= (
Section 11.1
Undefined terms
Point- A
Line (1D)- AB Two points determine a line
Plane (2D)
Collinear- set of points contained on a single line.
If not then considered noncollinear
Coplanar- set of points contained on a single plane.
If not considered no
Section 11.3
Possible properties of curves
Can be simple = no points redrawn except possible beginning and
ending
Can be closed= beginning points and ending point the same
EXAMPLES IN NOTES
Convex= must be simple and closed. And for every pair of point
Section 12.1
Triangle congruence
3!=6
Correspondence- way of pairing vertices
Definition of triangle congruence- two triangles are congruent if their
vertices can be paired in such a way that corresponding angles are
congruent and corresponding sides are
Section 11-4
Two angles are supplementary if their related angles sum to 180 degrees
Complementary if their related angles sum to 90 degrees
Vertical angles have to be congruent
Proof: m<2 and m<3 = 180 degrees
m<3 and m<4 = 180 degrees
m<2 and m<4 must
Section 12.2
More triangle congruence properties
ASA Angle Side Angle
o If two angles and the included side of one triangle are
congruent to the corresponding parts of a second triangle, the
triangles are congruent.
If you have ASA then you have AAS
AA
Section12.3
OtherConstructions
Givenapointonthelineandapointnotontheline,constructtheparallellineto
thegivenlinethroughthegivenpoint.
o Correspondinganglemethod
o
RhombusMethod
Constructthelineperpendiculartoagivenlineandcontainingapointthatis
o Onthelin
Section 11-5
Math 366 Lecture Notes
Section 11.5 Networks
Knigsberg Bridge Problem
Is it possible to walk across all the bridges so that each bridge is crossed exactly once on
the same walk?
The problem can be made simpler by representing the problem in a
Section 11-4
Math 366 Lecture Notes
Section 11.4 Geometry in Three Dimensions
Simple Closed Surfaces
A simple closed surface has exactly one interior, no holes, and is hollow.
A sphere is the set of all points at a given distance from a given point, the c
Section 11-3
Math 366 Lecture Notes
Section 11.3 More About Angles
Vertical angles are pairs of angles opposite each other at the intersection of two lines.
Theorem 11-1
Vertical angles are congruent.
Proof:
Supplementary angles are two angles, the sum of
Chapter 14
Math 366 Chapter 14 Review Problems
1. Draw a reflection of the following figure in l.
2. Draw a translation of the following figure, as indicated in the given vector.
3. Construct the image of ABC through a reflection in l.
l
A
B
C
Chapter 14
Section 12-4
Math 366 Lecture Notes
Section 12.4 Similar Triangles and Similar Figures
Two figures that have the same shape but not necessarily the same size are similar. The ratio of
the corresponding side lengths is the scale factor.
Similar Triangles
A
Section 12-6
Math 366 Lecture Notes
Section 12.6 Trigonometry Ratios via Similarity
The word trigonometry is derived from the Greek words tronom, which means triangle, and
metron, which means measurement. We will study the basic of right triangle trigonom
Section 13-1
Math 366 Lecture Notes
Section 13.1 Linear Measure
The English System
Originally, a yard was the distance from the tip of the nose to the end of an outstretched arm of
an adult person and a foot was the length of a human foot.
Unit
yard (yd)
Section 13-2
Math 366 Lecture Notes
Section 13.2 Areas of Polygons and Circles
Area is measured using square units and the area of a region is the number of nonoverlapping
square units that covers the region.
Length is given in units (i.e., inches)
Area i
Section 13-3
Math 366 Lecture Notes
Section 13.3 The Pythagorean Theorem and the Distance
Formula
Theorem 13-2 Pythagorean Theorem
If a right triangle has legs of lengths a and b and hypotenuse of length c, then c2 = a2 + b2.
A
c
a
C
b
B
a
b
a
b
The Grade
Section 13-4
Math 366 Lecture Notes
Section 13.4 Surface Areas
The grade 5 Focal Points state:
They (students) decompose three-dimensional shapes and find surface areas and volumes of
prisms. As they work with surface area, they find and justify relations
Section 13-5
Math 366 Lecture Notes
Section 13.5 Volume, Mass, and Temperature
Surface area is the number of square units covering a three-dimensional figure; volume describes
how much space a three-dimensional figure contains.
The unit of measure for vol
Section 14-1
Math 366 Lecture Notes
Section 14.1 Translations and Rotations
Translations
Any rigid motion that preserves length or distance is an isometry (meaning equal measure).
Any function from a plane to itself that is a one-to-one correspondence bet
Section 14-2
Math 366 Lecture Notes
Section 14.2 Reflections and Glide Reflections
Reflections
A reflection is an isometry in which a figure is reflected across a reflecting line, creating a
mirror image. Unlike a translation or rotation, the reflection r