Five-Minute Check (over Lesson 1–3) Mathematical Practices 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: Find the Angle Measure Lesson Menu

Use the number line to find the measure of AC. 5-Minute Check 1

Use the number line to find the measure of DE. C. 7 D. 9 5-Minute Check 2

Use the number line to find the midpoint of EG. A. D B. E C. F D. H 5-Minute Check 3

Find the distance between P(–2, 5) and Q(4, –3). 5-Minute Check 4

Find the coordinates of R if M(–4, 5) is the midpoint of RS and S has coordinates (0, –10). B. (–4, 15) C. (–2, –5) D. (2, 20) 5-Minute Check 5

A boat located at (4, 1) can dock at two locations 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

Mathematical Practices 5 Use appropriate tools strategically. 6 Attend to precision. Content Standards G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). MP

You measured line segments. Measure and classify angles. Identify and use congruent angles and the bisector of an angle. Then/Now

ray degree right angle acute angle opposite rays angle obtuse angle angle bisector opposite rays angle side vertex interior exterior Vocabulary

A. Name all angles that have B as a vertex. Angles and Their Parts A. Name all angles that have B as a vertex. Which angles have two noncollinear rays that meet at the same endpoint or vertex B? Answer: Example 1

Rays are the sides of the angles. What are the sides of ? Angles and Their Parts B. Name the sides of 5. Rays are the sides of the angles. What are the sides of ? Answer: Example 1

Angles and Their Parts C. When naming angles using three letters, the vertex must be the second of the three letters. You can name an angle using a single letter only when there is exactly one angle located at that vertex. Use letters to name Example 1

A. A. B. C. D. Example 1a

B. A. B. C. D. none of these Example 1b

Which of the following is another name for 3? B. C. D. Example 1c

Concept

A. Copy the diagram below, and extend each ray. Measure and Classify Angles A. Copy the diagram below, and extend each ray. Classify each angle as right, acute, or obtuse. Then use a protractor to measure the angle to the nearest degree.   Example 2

Measure and Classify Angles   Example 2

Measure and Classify Angles Example 2

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

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

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

Find the Angle Measure 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 mGBH and mHCI if GBH  HCI, mGBH = 2x + 5, and mHCI = 3x – 10. Example 3

mGBH = mHCI Definition of congruent angles Find the Angle Measure Step 1 Solve for x. GBH  HCI Given mGBH = mHCI 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

Step 2 Use the value of x to find the measure of either angle. Find the Angle Measure Step 2 Use the value of x to find the measure of either angle. . Answer: mGBH = 35, mHCI = 35 Example 3

Find mBHC and mDJE if BHC  DJE, mBHC = 4x + 5, and mDJE = 3x + 30. A. mBHC = 105, mDJE = 105 B. mBHC = 35, mDJE = 35 C. mBHC = 35, mDJE = 105 D. mBHC = 105, mDJE = 35 Example 3