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In this lesson, students will learn how to classify and measure angles, as well as identify the parts of an angle. They will use the number line and solve real-world problems involving angles.
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Five-Minute Check (over Lesson 1–3) Then/Now New Vocabulary Example 1: Real-World Example: Angles and Their Parts Key Concept: Classify Angles Example 2: Measure and Classify Angles Example 3: Measure and Classify Angles Lesson Menu
A B C D Use the number line to find the measure of AC. A. 2 B. 4 C. 6 D. 8 5-Minute Check 1
A B C D Use the number line to find the measure of DE. A. 3 B. 5 C. 7 D. 9 5-Minute Check 2
A B C D Use the number line to find the midpoint of EG. A.D B.E C.F D.H 5-Minute Check 3
A B C D Find the distance between P(–2, 5) and Q(4, –3). A. 12 B. 10 C. 5 D. 1 5-Minute Check 4
A B C D Find the coordinates of R if M(–4, 5) is the midpoint of RS and S has coordinates (0, –10). A. (–8, 20) B. (–4, 15) C. (–2, –5) D. (2, 20) 5-Minute Check 5
A B C D A boat located at (4, 1) can dock at two locations. Location A is at (–2, 9) and Location B is at (9, –11). Which location is closest? How many units away is the closest dock? A. Location A, 10 units B. Location A, 12.5 units C. Location B, 10 units D. Location B, 12.5 units 5-Minute Check 6
You measured line segments. (Lesson 1–2) • Measure and classify angles. • Identify and use congruent angles and the bisector of an angle. Then/Now
degree • right angle • acute angle • obtuse angle • angle bisector • ray • opposite rays • angle • side • vertex • interior • exterior Vocabulary
Answer: Angles and Their Parts A. Name all angles that have B as a vertex. Example 1
Answer: Angles and Their Parts B.Name the sides of5. Example 1
C. Angles and Their Parts Example 1
A B C D A. B. C. D. A. Example 1a
A B C D A. B. C. D.none of these B. Example 1b
A B C D A. B. C. D. Which of the following is another name for 3? C. Example 1c
Measure and Classify Angles A. Measure TYV and classify it as right, acute, or obtuse. Answer:mTYV = 90, so TYV is a right angle. Example 2
Measure and Classify Angles Answer:180 > mWYT > 90, so WYT is an obtuse angle. Example 2
Measure and Classify Angles Example 2
A B C D A.Measure CZD and classify it as right, acute, or obtuse. A. 30°, acute B. 30°, obtuse C. 150°, acute D. 150°, obtuse Example 2a
A B C D B.Measure CZE and classify it as right, acute, or obtuse. A. 60°, acute B. 90°, acute C. 90°, right D. 90°, obtuse Example 2b
A B C D C.Measure DZX and classify it as right, acute, or obtuse. A. 30°, acute B. 30°, obtuse C. 150°, acute D. 150°, obtuse Example 2c
Measure and Classify Angles INTERIOR 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. Example 3
Measure and Classify Angles Step 1 Solve for x. GBH HCI Given 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. Example 3
. Measure and Classify Angles Step 2 Use the value of x to find the measure of either angle. Answer:mGBH = 35, mHCI = 35 Example 3
A B C D Find mBHC and mDJE if BHC DJE, mBHC = 4x + 5, and mDJE = 3x + 30. A.mBHC = 105, mDJE = 105 B.mBHC = 35, mDJE = 35 C.mBHC = 35, mDJE = 105 D.mBHC = 105, mDJE = 35 Example 3