Lesson 1-4 Angle Measure

5-Minute Check on Lesson 1-3 Transparency 1-4 Click the mouse button or press the Space Bar to display the answers. Use the number line to find each measure. 1.AC 2.DE 3.Find the midpoint of EG 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: ACBD 12 units13 units17 units30 units D AC E DEFGH

5-Minute Check on Lesson 1-3 Transparency 1-4 Click the mouse button or press the Space Bar to display the answers. Use the number line to find each measure. 1.AC 2.DE 3.Find the midpoint of EG 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: ACBD 12 units13 units17 units30 units D AC E DEFGH 4 9 F 10 (-8, 20)

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 Ray VA Ray VB Vertex (hinge point) Interior of angle  AVB Exterior of angle Circle 360º Angles measured in degrees A degree is 1/360 th around a circle AcuteRightObtuse m  A < 90º A B m  A = 90º 90º < m  A < 180º A A A

Example 4-1a 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.

Example 4-1d a. Name all angles that have X as a vertex. b. Name the sides of  3. c. Write another name for  3. Answer:  1,  2,  3, and  RXB or  RXN Answer:  AXB,  AXN,  NXA,  BXA Answer:

Example 4-2a 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 4-2b Measure  WYT and classify it as right, acute, or obtuse. Use a protractor to find that. Answer: > is an obtuse angle.

Example 4-2d a.  CZD b.  CZE c.  DZX Answer: 150, obtuse Answer: 90, right Answer: 30, acute With lines ZE and CX and ray ZD, measure each angle named and classify it as right, acute, or obtuse. C Z X D E

Example 4-3d SIGNS A railroad crossing sign forms congruent angles. In the figure,  WVX =  ZVY. If m  WVX =7a + 13 and m  ZVY =10a – 20, find the actual measurements of  WVX and  ZVY.  WVX   ZVY 7a + 13 = 10a – 20 7a + 33 = 10a 33 = 3a 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