1. 1.4 ANGLES & THEIR MEASURES 1.Use Angle Postulates 2.Classify angles as acute, obtuse, right, or straight

2. WARM-UP: BILLIARDS (“POOL”) Who has played pool? What’s a “bank shot”? How do you know where to put the cue ball on the side? It’s all in the angles! Angles are the foundation of geometry The rest of this course depends on understanding angles!

3. ANGLE angle An angle consists of two rays that have the same initial point Vertex Sides (AB and AC) A B C sides The rays are the sides of the angle vertex The initial point is the vertex of the angle

4. ANGLE SYMBOL: Definition: 2 rays that share the same endpoint (or initial point) Y Z X Sides – the rays XY & XZ Vertex – the common endpoint; X Named <YXZ, <ZXY (vertex is always in the middle), or <X (if it’s the only <X in the diagram). Angles can also be named by a #. (<5) 5

5. EXAMPLE 1: NAMING ANGLES In the figure, there are three different angles (two smaller ones and a larger one) ALWAYS The vertex is ALWAYS in the middle of the name P S R Q  PQS or  SQP  RQS or  SQR  PQR or  RQP

6. THERE ARE 3 DIFFERENT <B’S IN THIS DIAGRAM; THEREFORE, NONE OF THEM SHOULD BE CALLED <B. A B C D Name the 3 angles…. <ABC or <CBA <ABD or <DBA <DBC or <CBD

7. PRACTICE 1: NAMING ANGLES Name all the angles in each figure below (a) (b) One angle only:  EFG or  GFE or  F Three angles:  ABC or  CBA  CBD or  DBC  ABD or  DBA

8. CONGRUENT ANGLES Angles that have the same measure are congruent angles. Just like segments: Measures can be equal (m  BAC = m  DEF) Angles can be congruent (  BAC   DEF) A B C 50° E D F angle congruence marks

9. 2. MEASURING ANGLES (POSTULATE 3) measurem  degrees (°) The measure of an angle (m  ) is written in units called degrees (°) We measure an angle with protractor a protractor Vertex goes here Line up one side… Measure other side 50°

10. POSTULATE 3: PROTRACTOR POST. (CONT.) The rays of an angle can be matched up with real #s (from 1 to 180) on a protractor so that the measure of the < equals the absolute value of the difference of the 2 #s. 55 o 20 o m<A = 55-20 = 35 o

11. EXAMPLE 2: MEASURE THE ANGLES 65° 125° 25°

12. 3. CLASSIFYING ANGLES

13. EXAMPLE 3: CLASSIFYING ANGLES a. m  G = 180°___________________ b. m  H=25°___________________ c. m  J=100°___________________ straight angle acute angle obtuse angle

14. ADJACENT ANGLES 2 angles that share a common vertex & side, but have no common interior parts. (they have the same vertex, but don’t overlap) such as <1 & <2 1 2

15. INTERIOR OR EXTERIOR? B is ___________ C is ___________ D is ___________ in the interior in the exterior on the < A B C D

16. ANGLE ADDITION POSTULATE Postulate 4: Angle Addition Postulate interior If P is in the interior of  RST,  RSP  PST then the measure of  RST (called m  RST) is the sum of the measure of  RSP and  PST R P T S m  RST = m  RSP + m  PST Interior Exterior

17. EXAMPLE 4: ADD ANGLES Find the measure of  FJH m  FJH = ________ m  FJH = m  FJG + m  GJH m  FJH = 35° + 60° 95°

18. PRACTICE : FIND ANGLE MEASURE Use the angle addition postulate to find m  ABD in each figure below (a)(b) m  ABD = _______ 110°60° (180° – 120°)(26° + 84°)

19. EXAMPLE: Name an acute angle <3, <2, <SBT, or <TBC Name an obtuse angle <ABT Name a right angle <1, <ABS, or <SBC Name a straight angle <ABC 1 2 3 A BC S T

20. CLOSURE: ANGLE ADDITION What are three names for this angle? What type of angle is it? What is the angle’s measure? What is m  RTU? 52° 28°

21. EXAMPLE USING PROTRACTORS Plot the Points A (-3, -1), B(-1,1), C (2,4), D(2,1) and E (2,-2). Then measure and classify the following angles as acute, right, obtuse, or straight. A. m<DBE= 45°; Acute B. m<EBC=90°; Right C. m<ABC=180°; Straight D. m<ABD= 135°; Obtuse

22. ASSIGNMENT Ch 1.4 (pg. 29-31) #18-48 EVEN