Lesson 1-4
Angle Measure
Lesson Outline
Five-Minute Check
Then & Now and Objectives
Vocabulary
Key Concept
Examples
Lesson Checkpoints
Summary and Homework
Then and Now
You measure line segments (Lesson 1–2)
• Measure and classify angles
• Identify and use congruent angles an the bisector of an angle
Objectives
• Measure and classify angles• Obtuse – m > 90• Right – m = 90 (the corner of a piece of paper)• Acute – m < 90
• Identify and use congruent angles an the bisector of an angle
Vocabulary• Degree – one three hundred and sixtieth of a circle• Ray – part of a line with one end point• Opposite rays – are collinear rays with the same end
point (& form a 180 degree angle)
Angle is formed by 2 noncollinear rays with a common endpoint (vertex)
• Sides – composed of rays• Vertex – is the common endpoint• Interior – area between the two rays that form the
angle• Exterior – area not between the two rays that form
the angle
Vocabulary (cont)
Special types of angles:– Right angle – measure equals 90 degrees
– Acute angle – measure is less than 90 degrees
– Obtuse angle – measure is greater than 90 degrees (but less than 180)
• Angle Bisector – a ray that divides an angle into two congruent angles
Example 1
Name all angles that have B as a vertex.
Answer: 5, 6, 7, and ABG
Name the sides of 5.
Answer: and or are the sides of 5.
Write another name for 6.
Answer: EBD, FBD, DBF, and DBE are other names for 6.
Key Concept
• An easy measuring device is the corner of a piece of notebook paper (or computer paper). It is a right angle.
Example 2a
Measure TYV and classify it as right, acute, or obtuse.
TYV is marked with a right angle symbol, so measuring is not necessary.
Answer: is a right angle.
Example 2b
Measure WYT and classify it as right, acute, or obtuse.
Use a protractor to find that .
Answer: >is an obtuse angle.
Example 2c
Measure TYU and classify it as right, acute, or obtuse.
Use a protractor to find that m TYU = 45° .
Answer: Since 45 < 90, then TYU is an acute angle.
Example 3INTERIOR DESIGN Wall stickers of standard shapes are often used to provide a stimulating environment for a young child’s room. A five-pointed star sticker is shown with vertices labeled. Find mGBH and mHCI if GBH HCI, mGBH = 2x + 5, and mHCI = 3x – 10.
GBH HCI Given
Step 1 Solve for x.
Example 3 cont
mGBH = mHCI Definition of congruent angles
2x + 5 = 3x – 10 Substitution
2x + 15 = 3x Add 10 to each side.
15 = x Subtract 2x from each side.
Step 2 Use the value of x to find the measure of either angle.
Answer: mGBH = 35, mHCI = 35
mGBH = 2x + 5 Given
= 2(15) + 5 Substitution, x = 15
= 30 + 5 = 35 Simplify.
Lesson Checkpoints
Summary & Homework
• Summary:– Angles are named by 3 points with the vertex in
the middle (or by vertex letter if no confusion)– Angles are classified as acute, right, or obtuse
according to their measure– An angle bisector is a ray that divides an angle
into two congruent angles (halves)• Ray is equidistance from the sides of the angle
• Homework: – pg 41-3: 30-35, 39-42