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Lesson Menu Five-Minute Check (over Lesson 1–3) CCSS 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

Over Lesson 1–3 5-Minute Check 1 A.2 B.4 C.6 D.8 Use the number line to find the measure of AC.

Over Lesson 1–3 5-Minute Check 2 A.3 B.5 C.7 D.9 Use the number line to find the measure of DE.

Over Lesson 1–3 5-Minute Check 3 A.D B.E C.F D.H Use the number line to find the midpoint of EG.

Over Lesson 1–3 5-Minute Check 4 A.12 B.10 C.5 D.1 Find the distance between P(–2, 5) and Q(4, –3).

Over Lesson 1–3 5-Minute Check 5 A.(–8, 20) B.(–4, 15) C.(–2, –5) D.(2, 20) Find the coordinates of R if M(–4, 5) is the midpoint of RS and S has coordinates (0, –10).

Over Lesson 1–3 5-Minute Check 6 A.Location A, 10 units B.Location A, 12.5 units C.Location B, 10 units D.Location B, 12.5 units 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?

CCSS 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.). Mathematical Practices 5 Use appropriate tools strategically. 6 Attend to precision.

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

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

Example 1 Angles and Their Parts A. Name all angles that have B as a vertex. Answer:

Example 1 Angles and Their Parts Answer: B. Name the sides of  5.

Example 1 Angles and Their Parts C.

Example 1a A. B. C. D.

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

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

Concept

Example 2 Measure and Classify Angles A. Measure  TYV and classify it as right, acute, or obtuse. Answer: m  TYV = 90, so  TYV is a right angle.

Example 2 Measure and Classify Angles Answer: 180 > m  WYT > 90, so  WYT is an obtuse angle.

Example 2 Measure and Classify Angles

Example 2a A.30°, acute B.30°, obtuse C.150°, acute D.150°, obtuse A. Measure  CZD and classify it as right, acute, or obtuse.

Example 2b A.60°, acute B.90°, acute C.90°, right D.90°, obtuse B. Measure  CZE and classify it as right, acute, or obtuse.

Example 2c A.30°, acute B.30°, obtuse C.150°, acute D.150°, obtuse C. Measure  DZX and classify it as right, acute, or obtuse.

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

Example 3 Measure and Classify Angles  GBH   HCIGiven m  GBH= m  HCIDefinition of congruent angles 2x + 5= 3x – 10Substitution 2x + 15= 3xAdd 10 to each side. 15= xSubtract 2x from each side. Step 1 Solve for x.

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

Example 3 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 Find m  BHC and m  DJE if  BHC   DJE, m  BHC = 4x + 5, and m  DJE = 3x + 30.

End of the Lesson