(And Introduction to Measuring Angles)

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(And Introduction to Measuring Angles)
Lesson 1.1 (And Introduction to Measuring Angles) Objective: Recognize points, lines, line segments, rays, angles, and triangles, and measure segments, angles, and classify angles

All lines are straight and extend infinitely far in both directions.
Basic Definitions Points: Represented by capital letters (Draw 3 points and label them) Lines: Lines are made up of points and are straight. Arrows are drawn on the ends to show that the lines extend infinitely far in both directions. All lines are straight and extend infinitely far in both directions.

Lines can be named based on any two points.
Basic Definitions More on Lines: Lines can be named based on any two points. Let’s take a look at an example: Name the line in 3 different ways. B l A

Basic Definitions Number Line:
A number line is formed when a numerical value is assigned to each point on a line. Example: Draw a number line from -2 to 3 using one tick mark per integer.

Line Segments are named by their endpoints.
Basic Definitions Line Segment: Like lines, segments are made up of points and are straight, however, segments have a definite beginning and end. Line Segments are named by their endpoints. Examples: Name the following line segments S P R X Q

Like lines and segments, rays are made up of points and are straight.
Basic Definitions Rays: Like lines and segments, rays are made up of points and are straight. A ray differs from a line or segment in that it begins at an endpoint and extends infinitely far in only one direction. Examples: M D K P J C L

Name the following rays:
Note: It is important to keep in mind that when we name a ray, we name the endpoint first! This makes it clear as to where the ray begins. Name the following rays: M D K P J C L

Two rays that have the same endpoint form an angle.
Basic Definitions Angles: Two rays that have the same endpoint form an angle. Def. An Angle is made up of two rays with a common endpoint. This point is called the vertex of the angle. The rays are called sides of the angle. Examples: P T B 1 A 2 2 C H S

Naming Angles When naming an angle with 3 letters you must name the vertex in the middle! Every time…no exceptions! Examples: Name the following angles P T B 1 A 2 2 C H S

Example #1 a. b. c. A E B C D m

Draw a diagram in which the intersection of with is segment
Example #2 Draw a diagram in which the intersection of with is segment

Measuring Segments Segments can be measured using tools such as rulers or meter sticks, and often, segments found on number lines can be measured by subtracting the ending and starting value. Example: P Q

Measuring Angles Angles are measured using Protractors, and in this course we will be measuring angles in degrees. The measure (or size) of an angle is the amount of turning you would do if you were at the vertex, looking along one side, and then turned to look along the other side. (A surveyor’s transit works in a similar way!)

Classifying Angles by Size
Angles can be classified into four groups: Name Acute Angles Obtuse Angles Right Angles Straight Angles Definition An angle whose measure is greater than 0 and less than 90° 0< x < 90° An angle whose measure is greater than 90° and less than 180° 90°<x<180° An angle whose measure is 90° An angle whose measure is 180° Picture

Homework Lesson 1.1 Worksheet

Measurement of Segments and Angles
Lesson 1.2 Measurement of Segments and Angles Objective: Measure segments, angles, classify angles by size, name the parts of a degree, recognize congruent angles and segments

Recap… Yesterday we touched briefly on measuring segments and angles, and classifying angles Today, we are going to break down measuring angles into degrees, minutes, and seconds and discuss angle congruencies.

Recap Practice <B is acute. What are the restrictions on m<B?
What are the restrictions on x? (2x + 14)° B

S’More Practice <ABC is a right angle <1 = (3x + 4)°
Find: m<1 1 2 B C

Parts of a Degree Every hour of the day is divided into 60 minutes.
Each minute is divided into 60 seconds. Similarly, each degree of an angle is divided into 60 minutes. And each minute of an angle is divided into 60 seconds. 60’ = 1° 60” = 1’

Practice… 87½° = 60.4° = 90° = 180° = ½ of a degree is ½ of 60’= 30’

Clock Handout Time! Important Notes:
A circle = 360°, and 360 ÷ 12 = 30° Every 15 minutes the hour hand moves ¼ of 30° (that’s 7.5°) One way to determine how many degrees the hour hand has moved is to calculate what fraction (out of 60 minutes) your minute hand is at. …. Let’s try this

Find the measure of the angle formed by the hands of a clock at 11:40
Example #1: Find the measure of the angle formed by the hands of a clock at 11:40 Between 8 and 9 = 30° Between 9 and 10 = 30° Between 10 and 11 = 30° Total = 90°

Find the measure of the angle formed by the hands of a clock at 11:40
Example #1: Find the measure of the angle formed by the hands of a clock at 11:40 Now we have to consider the 40 minutes. 40/60 = 2/3 (So the hour hand has moved 2/3 of the way between 11 and 12) 2/3 of 30° = 20° Final Answer: 90° + 20° = 110 °

Example #2: Given: <ABC is a right angle <ABD = 67°21’37”
Find: <DBC A D B C Label your diagram and think about how 90° is written in degrees, minutes, and seconds!

Congruent Angles and Segments
Def. Congruent ( ) angles are angles that have the same measure Def. Congruent ( ) segments are segments that have the same measure S 42° P B 42° 3 cm 3 cm R A X

We use identical tick marks to indicate congruent angles and segments.
Example #3: Name the 4 pairs of congruent parts S G Z Y ^ K ^ R T W X H

Homework Lesson 1.2 Worksheet