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Mr. Wolf Friday 9/12/08 Geometry Grades 10-12 Unit 1: Points, Lines, Planes, and Angles Angles II Materials and Resources: Warm-up (1 per student) How to Measure with a Protractor (1 per student) Graph paper (1 per student) Measuring with a Protractor sheet (1 per student) Two Postulates and Special Pairs of Angles (1 per student) Weekly Self-Assessments (1 per student) PA Standards Addressed: 2.3.8 C. Measure angles in degrees and determine relations of angles. Instructional Objectives: Students will be able to measure angles using a protractor in order to identify acute, obtuse, right, straight, congruent, and adjacent angles, and angle bisectors. Students will be able to define and apply the Protractor Postulate, Angle Addition Postulate, and Theorem 2-3. Students will be able to identify and define complementary, supplementary, and vertical angles. Time Activity Description 10 min Warm-up Pass out the warm-up exercise and review solutions. 5 min Homework Check Spot-check student homework exercises. 10 min Homework Review Provide solutions to homework and answer any student questions. 10 min How to Use a Modeling: Pass out the graph paper, protractors, and Protractor Measuring with a Protractor sheet. Show students the proper way to use a protractor with the help of the SmartBoard file. 10 min Measuring with a Guiding: Help students complete the activity. Protractor Independent Practice: Measuring Angles Activity Activity Assessment: Review solutions. Modifications: Students with special needs will be given pre-drawn figures to measure. Advanced students will be asked to draw their figures on the board or overhead. 5 min Two Postulates and Modeling: Present the two angle postulates. Special Pairs of Guiding: Help students complete the activity. Angles sheet Independent Practice: Measuring Angles Activity 1. Assessment: Review solutions. 10 min Measuring with a Modifications: Protractor Students with special needs will be given pre-drawn Activity #1 figures to measure. 10 min Two Postulates and Special Pairs of Angles sheet 10 min Measuring with a Protractor Activity #2 10 min Measuring with a Protractor Activity #3 10 min Conclusion Homework: None – weekend! Lesson Reflection: Advanced students will be asked to draw their figures on the board or overhead. Modeling: Present the three definitions (supplementary, complementary, and vertical angles). Guiding: Help students complete the activity. Independent Practice: Measuring Angles Activity 2. Assessment: Review solutions. Modifications: Students with special needs will be given pre-drawn figures to measure. Advanced students will be asked to draw their figures on the board or overhead. Modeling: Provided during lesson. Guiding: Help students complete the activity. Independent Practice: Measuring Angles Activity 2. Assessment: Review solutions. Modifications: Students with special needs will be given pre-drawn figures to measure. Advanced students will be asked to draw their figures on the board or overhead. Weekly Self-Assessments Geometry Fall 2008 Name: ________________________ Warm-up 1) What three figures make up an angle? 2) What is the name of an angle whose measure is between 1°-89°? 3) How many degrees are in a right angle? 4) How many degrees are in a straight angle? 5) What does an angle bisector do to an angle? 6) What makes two angles congruent? ------------------------------------------------------------------------------------------------------------ Geometry Fall 2008 Name: ________________________ Warm-up 1) What three figures make up an angle? 2) What is the name of an angle whose measure is between 1°-89°? 3) How many degrees are in a right angle? 4) How many degrees are in a straight angle? 5) What does an angle bisector do to an angle? 6) What makes two angles congruent? Geometry Fall 2008 Name: ________________________ How to Measure with a Protractor Step 1: Identify the angle (two rays and shared vertex) that you would like to measure. Step 2: Place the straight edge of the protractor along one of the rays so that the vertex of the angle is directly in the middle of this edge (there is a hole in the protractor that the vertex should line up with) Step 3: The measure of the angle is the number on the protractor where that the other ray lands upon (extend the line to reach the edge of the protractor if necessary) Be careful! If the angle is acute, use the smaller number (between 0°-90°). If the angle is obtuse, use the larger number (between 90°-180°) Examples: Geometry Fall 2008 Name: ________________________ Measuring with a Protractor Activity #1: Protractor Postulate 1) Find the location of ray BD and ray BE on a protractor by lining the straight edge with the line AC with the protractor hole over vertex B. 2) Use the Protractor Postulate to find mDBE . Angle Addition Postulate 1) Using a protractor, find mMON and mNOP . mMON = _________ mNOP = _________ 2) Apply the Angle Addition Postulate and calculate mMOP . 3) Confirm your answer by measuring MOP with a protractor. mMOP =_________ Activity #2: Special Pairs of Angles 1) Using a protractor, find mKLI and mGHJ mKLI = _________ mGHJ = _________ 2) Are these angles complementary, supplementary, or vertical? 3) How do you know? Special Pairs of Angles 1) Using a protractor, find mABC and mEFD mABC = _________ mEFD = _________ 2) Are these angles complementary, supplementary, or vertical? 3) How do you know? Special Pairs of Angles 1) Using a protractor, measure angles 1, 2, 3, and 4 m1= _________ m2 = _________ m3 = _________ 2) What kind of angles are 1 and 3? 2 and 4? 3) How do you know? m4 = _________ Activity #3: Angles in Shapes 1) Using a protractor, find the following angle measures: mTUV = _________ mUTV = _________ mTVU = _________ 2) Add the three angle measures together. What do you get? __________ Angles in Shapes 1) Using a protractor, find the following angle measures: mABD = _________ mACD = _________ mCDB = _________ mBAC = _________ 2) Add the four angle measures together. What do you get? __________ 3) Do you notice anything between this total angle measure and the total angle measure you found for triangle TUV? Geometry Fall 2008 Name: ________________________ Two Postulates and Special Pairs of Angles Protractor Postulate: m ABC x y Angle Addition Postulate: IF point B lies in the interior of AOC THEN mAOB mBOC mAOC . IF AOC is a straight angle and B is any point not on AC THEN mAOB mBOC 180 complementary angles - supplementary angles - vertical angles - Weekly Self-Assessment Name: _______________________ Class: __________ Date: __________ Directions: Please fill out the following prompts and describe your learning experiences during this week’s class. Be honest! These sheets are not graded and are used to refine and improve lessons for the future. 1. This week I have learned… 2. This week I successfully… 3. But I had difficulty with… 4. My favorite part(s) of this week…. ------------------------------DO NOT WRITE BELOW THIS LINE-----------------------------Teacher Comments/Evaluation: