Download Unit 1: Foundations of Geometry

Unit 1: Foundations of Geometry
Name: ___________________________ Hour: ___
1.1 Understanding Points, Lines, and Planes
Vocabulary
Point:
Line:
Line Segment:
Ray:
Opposite Ray:
Endpoint:
Plane:
Collinear:
Coplanar:
Whole Class Examples: Follow the directions for the problems below.
1. Answer the following questions below:
a) How many points must exist in order to make a line?
b) How many points must exist in order to make a plane? Must they be collinear?
c) How many intersection points occur when two lines intersect?
d) When two planes intersect what do they form?
2. Draw an example of the following situations
a) Segment DC
b) E, F, G, H are coplanar points
c) Line R, S
3.
a) Name four coplanar points using the figure to the right
b) Name two opposite rays (add a reference point if needed)
c) Name four lines in the figure to the right
4. Write and draw Real-Life Examples of the following terms
1. Point
2. Line
3 Plane
4. Segment
6. Ray
5. Endpoint
Practice: Follow the directions for the problems below.
1. What does undefined mean?
a) Which terms above do you feel are undefinable?
2.
a) Name a set of non-collinear points
b) Name a ray
c) Name a segment
3. What is the greatest number of intersection points 4 coplanar lines can have? Draw an example.
a) 0
b) 2
c) 4
d) 6
4. Line AB = Line BA true or false? Draw an example.
Think About The Situation (TATS): Sometimes, always, never: If two rays share a common endpoint
then they form a line? Draw an example to support your answer.
1.2 Measuring and Constructing Segments
Vocabulary
Distance
Length
Midpoint
Congruent
Congruent Segments
Bisect
Segment Bisector
Construction
Segment Addition Postulate
Constructions:
1. Constructing Congruent Segments:
2. Bisecting a Segment:
3. Whole Class Examples:
B is between C and E. 𝐶𝐸 = 17.1
and 𝐷𝐸 = 8, find CD.
B is the midpoint of AC, if AB = 10
what is the length of AC?
AC and CF are congruent. If 𝐴𝐶 =
10, and 𝐶𝐹 = 2𝑥 what is the value
of x?
Practice: Follow the directions for the problems below.
1. M is between N and O. Find NO.
2. D is the midpoint of EF, ED = 4x + 6, and DF = 7x – 9. Find ED, DF, and EF.
3. If 𝐴𝐵 = 10 𝑐𝑚, place point C so that it is ¾ 𝑜𝑓 𝐴𝐵.
Think About The Situation (TATS): Explain the following…
1. Suppose R is the midpoint of ST, explain how SR and ST are related. Diagram this.
2. How are drawing and constructing similar? How are they different?
1.3 Measuring and Constructing Angles
Vocabulary
Angle (vertex, interior, exterior)
Measure
Degree
Congruent Angles
Acute Angle
Angle Bisector
Right Angle
Angle Addition Postulate
Constructions:
1. Constructing Congruent Angles:
2. Bisecting an Angle:
Obtuse Angle
Straight Angle
3. Whole Class Examples:
Ray ST bisects ∠𝐾𝑆𝑈. If ∠𝐾𝑆𝑈 =
75, what is the measure of ∠𝐾𝑆𝑇?
If 𝑚∠𝐷𝐸𝐹 = 48° and 𝑚∠𝐹𝐸𝐺 =
67°, Find 𝑚∠𝐷𝐸𝐺
Angles XYW and WYZ form a
complementary angle. If
𝑚∠𝑊𝑌𝑍 = 2𝑥 & 𝑚 ∠𝑋𝑌𝑊 = 3𝑥
find the value of x.
Practice: Follow the directions for the problems below.
1. Angles XYW and WYZ form a linear pair. If 𝑚∠𝑊𝑌𝑍 = 2𝑥 − 5 and 𝑚 ∠𝑋𝑌𝑊 = 3𝑥 + 10 find the value
of x.
2. If 𝑚∠𝑋𝑊𝑍 = 5𝑥 + 20° and 𝑚∠𝑋𝑊𝑌 = 3𝑥 + 10° and 𝑚∠𝑌𝑊𝑍 = 𝑥 + 30.
4. KM bisects ∠𝐽𝐾𝐿, 𝑚∠𝐽𝐾𝑀 = (4𝑥 + 6) °, and 𝑚∠𝑀𝐾𝐿 = (7𝑥 – 12) °. Find 𝑚∠𝐽𝐾𝑀.
Think About The Situation (TATS): Explain the following…
1. The measure of an obtuse angle is 5x + 45 what is the largest value for x?
1.4 Pairs of Angles
Vocabulary
Adjacent Angles
Linear Pair
Complementary Angle
Supplementary Angles
Vertical Angles
Whole Class Examples: Follow the directions for the problems below.
1. Draw an example of the following situations
a) Right Angle ABC
b) Complementary angles RST and UVX
c) Lines AB and CD intersect at point E to form vertical angles 1, 2, 3, and 4.
2. Use the figure to the right.
a) Give an example of an acute angle
b) Give an example of vertical angles
c) Give a set of angles that form a linear pair
3. Write and draw Real-Life Examples of the following terms
1. Adjacent Angles
2. Linear Pair
3. Vertical Angles
4. Complementary Angles
5. Supplementary Angles
6. Straight Angle
Practice: Follow the directions for the problems below.
1. How does the definition of “adjacent” help us in defining adjacent angles?
a) Can you use the same method in defining any other vocabulary terms from above?
2. Find the value of the variable below.
a) Find the complement of (7𝑥 – 12)°. Find the supplement.
b) 𝐴𝑛𝑔𝑙𝑒 𝐴 = 7𝑥 + 10 and 𝐴𝑛𝑔𝑙𝑒 𝐵 𝑖𝑠 31, find the value of x.
Think About The Situation (TATS): True or false, if false explain why…
1. A pair of vertical angles may also form a linear pair.
2. If an angle is acute then its complement should be greater than its supplement.
1.6 Midpoint and Distance in the Coordinate Plane
Vocabulary
Coordinate Plane
Midpoint Formula
Right Triangle (legs and hypotenuse)
Pythagorean Theorem
Midpoint Examples: Follow the directions for the problems below.
1. Calculate the midpoint of the following segments shown on the graphs below. Write your answer as an
ordered pair.
a.
b.
c.
2. Solve the following midpoint problems below.
a. What is the other endpoint of a segment if one endpoint is at (2, 5) and its midpoint is at (5, 1)?
b. What is the ordered pair of the point that is one-forth of the way from (2, 4) to (10,8)?
Distance Examples: Follow the directions for the problems below.
1. Calculate the distance of the segments in the graphs below.
a.
b.
c.
2. Solve the following distance problems below.
a. What is the distance of a segment with endpoints (0, -2) and (-5, -1)?
b. If a segment begins at (-2, 2) and is 7 units long, what are four possible coordinates for
its other endpoint?
c. The four bases on a baseball field form a
square with 90ft sides. The center of the pitching
mound has coordinates (42.8, 42.8). When a
pitcher throws from the center of the mound to
home plate, what is the distance of the throw, to
the nearest tenth?