Lesson 1 4 Angle Measure Transparency 1 4

Lesson 1 -4 Angle Measure

Transparency 1 -4 5 -Minute Check on Lesson 1 -3 Use the number line to find each measure. 1. AC D -4 2. DE -2 A 0 E C 2 4 6 3. Find the midpoint of EG 8 D 10 E F G H 4. Find the distance between P (-2, 5) and Q (4, -3). 5. Find the coordinates of R, if M (-4, 5) is the midpoint of RS and S has coordinates of (0, -10)? 6. What is the perimeter of ∆ DEF if its vertices are D(-2, -6), E(-2, 6), and F(3, -6)? Standardized Test Practice: A 12 units B 13 units C 17 units Click the mouse button or press the Space Bar to display the answers. D 30 units

Transparency 1 -4 5 -Minute Check on Lesson 1 -3 Use the number line to find each measure. 1. AC 4 2. DE 9 D -4 3. Find the midpoint of EG -2 A 0 E C 2 4 6 F 8 D 10 E F G H 4. Find the distance between P (-2, 5) and Q (4, -3). 10 5. Find the coordinates of R, if M (-4, 5) is the midpoint of RS and S has coordinates of (0, -10)? (-8, 20) 6. What is the perimeter of ∆ DEF if its vertices are D(-2, -6), E(-2, 6), and F(3, -6)? Standardized Test Practice: A 12 units B 13 units C 17 units Click the mouse button or press the Space Bar to display the answers. D 30 units

Objectives • Measure and classify angles • Identify and use congruent angles and 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

Angles Exterior of angle A R Vertex (hinge point) 360º A V ay Circle Interior of angle AVB Ray VB B Angles measured in degrees A degree is 1/360 th around a circle Acute A m A < 90º Right Obtuse A A m A = 90º < m A < 180º

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.

a. Name all angles that have X as a vertex. Answer: 1, 2, 3, and RXB or RXN b. Name the sides of 3. Answer: c. Write another name for 3. Answer: AXB, AXN, NXA, BXA

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.

Measure WYT and classify it as right, acute, or obtuse. Use a protractor to find that. Answer: > is an obtuse angle.

With lines ZE and CX and ray ZD, measure each angle named and classify it as right, acute, or obtuse. a. CZD Answer: 150, obtuse E D b. CZE X C Answer: 90, right c. DZX Answer: 30, acute Z

SIGNS A railroad crossing sign forms congruent angles. In the figure, WVX = ZVY. If m WVX =7 a + 13 and m ZVY =10 a – 20, find the actual measurements of WVX and ZVY. WVX ZVY 7 a + 13 = 10 a – 20 7 a + 33 = 10 a 33 = 3 a 11 = a WVX = 7(11) + 13 = 90° Answer: Both WVX and ZVY measure 90°

Summary & Homework • Summary: – 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) • Homework: pg 33 -35; 9, 11, 13, 14, 20, 24 -26, 50