1. Daily Warm Up Find the Area of quadrilateral with vertices A(4,3), B(- 2,5), C(-7,-2)

2. 1.5 Measuring and Constructing Angles

3. Vocabulary An angle is a set of points consisting of two differnet rays that share the same endpoint, called the vertex. The rays are the sides of the angle. A B C 1 sides vertex This angle can be name: With its vertex, such as <A With a point on each ray and the vertex, such as <BAC or <CAB With a number, such as <1

4. A lighthouse keeper measures the angles formed by the lighthouse and three boats. Name the three angles shown in the diagram L S R C <SLR or <RLS <RLC or <CLR <SLC or <CLS EXAMPLE 1

5. You try! Write three names for the angle. 1)2) P Q R X Y Z 1 <RQP <PQR <Q <XYZ <ZYX <Y <1

6. Vocabulary Interior of the Angle— the region that contains all the points between the sides of the angle. Exterior of the Angle—the region that contains all the points outside of the angle.

7. Types of Angles

8. EXAMPLE 2 Measure and classify angles Use the diagram to find the measure of the indicated angle. Then classify the angle. a. < KHJ b. <GHK c. <GHJ d. <GHL A protractor has an inner and an outer scale. When you measure an angle, check to see which scale to use.

9. a)<KHJ b)<GHK c)<GHJ d)<GHL

10. Angle Addition Postulate If P is in the interior of <RST, then the measure of <RST is equal to the sum of the measures of <RSP and <PST. <RST = <PSP + <PST R S T P

11. Congruent Angles Angles with the same measure Angles are Congruent & Measure of Angles are equal.

12. Angle Bisector A ray that divides an angle into two angles that are congruent.

13. EXAMPLE 3 Find angle measures ALGEBRA Given that m < LKN =145°, find m <LKM and m < MKN. 2x + 10 + 4x – 3 = 145

14. You Try! Find the indicated angle measures. Given that m< KLM is a straight angle, find m< KLN and m <NLM. ANSWER 125°, 55°

15. You Try! Given that m< EFG is a right angle, find m < EFH and m <HFG. ANSWER 60°, 30°

16. Example 4 Identify all pairs of congruent angles in the diagram. Use the diagram shown. <T and <S, < P and < R. ANSWER

17. Example 5 In the diagram, m < PQR = 130, m < QRS = 84, and m <TSR = 121. Find the other angle measures in the diagram. o Use the diagram shown. m < PTS = 121°, m < QPT = 84° ANSWER

18. EXAMPLE 6 In the diagram at the right, YW bisects < XYZ, and m < XYW = 18. Find m<XYZ. By the Angle Addition Postulate, m <XYZ = m < XYW + m<WYZ. Because YW bisects < XYZ you know that < XYW = < WYZ. 18 + 18 = 36°