Transcript Ch 9, Spatial Thinking

Introduction to Geometry: Points, Lines, and Planes
Lesson 9-1
Pre-Algebra
Additional Examples
Use the figure to name each of the following.
a. four points
H, I, J, and K
Name a point with a capital letter.
b. four different segments
HO, HJ , KI, and OI
Name a segment by its endpoints.
c. five other names for KI
IK , KO, OK , IO , and OI
There is one line pictured. It has several names.
d. five different rays
HO, OJ, KI , OK , and JH
The first letter names the endpoint of the ray.
Introduction to Geometry: Points, Lines, and Planes
Lesson 9-1
Pre-Algebra
Additional Examples
You are looking directly down into a wooden crate. Name
each of the following.
a. four segments that intersect PT
MP, OP, QT, ST
b. three segments parallel to PT
MQ, NR, OS
c. four segments skew to PT
MN, NO, QR, RS
Introduction to Geometry: Points, Lines, and Planes
Lesson 9-1
Pre-Algebra
Additional Examples
Draw two intersecting lines. Then draw a segment that is
parallel to one of the intersecting lines.
Use the lines on notebook or graph paper.
First draw two lines that intersect.
Then draw a segment that is parallel to one of
the lines.
Angle Relationships and Parallel Lines
Lesson 9-2
Pre-Algebra
Additional Examples
Find the measure of
m
m
3+m
4 = 180°
3 + 110° = 180°
m 3 + 110° – 110° = 180° –
110°
m 3 = 70°
3 if m
4 = 110°.
3 and
4 are supplementary.
Replace m
4 with 110°.
Solve for m
3.
Angle Relationships and Parallel Lines
Lesson 9-2
Pre-Algebra
Additional Examples
In the diagram, p || q. Identify each of the following.
a. congruent corresponding angles
1
3,
2
4,
5
7,
6
b. congruent alternate interior angles
2
7,
6
3
8
Classifying Polygons
Lesson 9-3
Additional Examples
Classify the triangle by its sides and angles.
The triangle has no congruent sides and one obtuse angle.
The triangle is a scalene obtuse triangle.
Pre-Algebra
Classifying Polygons
Lesson 9-3
Additional Examples
Name the types of quadrilaterals that have at least
one pair of parallel sides.
All parallelograms and trapezoids have at least one pair of
parallel sides.
Parallelograms include rectangles, rhombuses, and squares.
Pre-Algebra
Classifying Polygons
Lesson 9-3
Pre-Algebra
Additional Examples
A contractor is framing the wooden deck shown below in the
shape of a regular dodecagon (12 sides). Write a formula to find the
perimeter of the deck. Evaluate the formula for a side length of 3 ft.
To write a formula, let x = the length of each side.
The perimeter of the regular dodecagon is
x + x + x + x + x + x + x + x + x + x + x + x.
Therefore a formula for the perimeter is P = 12x.
P = 12x
Write the formula.
= 12(3)
Substitute 3 for x.
= 36
Simplify.
For a side length of 3 ft, the perimeter is 36 ft.
Problem Solving Strategy: Draw a Diagram
Lesson 9-4
Pre-Algebra
Additional Examples
How many diagonals does a nonagon have?
One strategy for solving this problem is to draw a diagram and
count the diagonals. A nonagon has nine sides.
You can draw six diagonals from one vertex of a nonagon.
AH, AG, AF, AE, AD, and AC are
some of the diagonals.
Problem Solving Strategy: Draw a Diagram
Lesson 9-4
Additional Examples
Pre-Algebra
(continued)
You can organize your results as you
count the diagonals. Do not count a
diagonal twice. (The diagonal from A to
C is the same as the one from C to A.)
Then find the sum of the numbers
of diagonals.
A nonagon has 27 diagonals.
Vertex Number of Diagonals
6
A
6
B
5
C
4
D
E
3
F
2
G
1
H
0
I
0
Total
27
Congruence
Lesson 9-5
Pre-Algebra
Additional Examples
In the figure,
TUV
WUX.
a. Name the corresponding congruent angles.
X, T
W , TUV
WUX
V
b. Name the corresponding congruent sides.
TV
WX , TU
WU , VU
XU
c. Find the length of WX.
Since WX,
TV, and TV = 300 m, WX = 300 m.
Congruence
Lesson 9-5
Pre-Algebra
Additional Examples
List the congruent corresponding parts of each pair of
triangles. Write a congruence statement for the triangles.
a.
ACB
AC
ECD
EC
Angle
Side
CAB
CED
Angle
ACB
ECD by ASA.
Congruence
Lesson 9-5
Pre-Algebra
Additional Examples
(continued)
b.
MK
MKJ
JK
MKJ
LJ
LJK
JK
Side
Angle
Side
LJK by SAS.