Chapter 7: GEOMETRY Section 2 Identifying and Classifying Angles

California Standards Measurement and Geometry 2.0: Students identify and describe the properties of 2- dimensional figures. Measurement and Geometry 2.1: Identify angles as VERTICAL, ADJACENT, COMPLEMENTARY, or SUPPLEMENTARY and provide descriptions of these terms. Measurement and Geometry 2.2: Use the Properties of Complementary and Supplementary Angles to solve problems involving an Unknown Angle

Key Vocabulary ANGLE: A figure formed by two rays with a shared vertex or common endpoint. VERTEX: The point of intersection of two sides of an angle. ACUTE ANGLE: An angle that measures between 0° and 90°. OBTUSE ANGLE: An angle that measures between 90° and 180°. RIGHT ANGLE: An angle that measures EXACTLY 90°. STRAIGHT ANGLE: An angle that measures EXACTLY 180° COMPLEMENTARY ANGLES: 2 angles that measure 90°. SUPPLEMENTARY ANGLES: 2 angles that measure 180°. ADJACENT ANGLES: Angles that lay side to side and share a vertex. VERTICAL ANGLES: Angles that are formed by intersecting lines and are OPPOSITE of each other. CONGRUENT ANGLES: Angles that EQUAL each other in measure.

What is an ANGLE? An ANGLE is a figure formed by two rays with a common endpoint. Angles can be measured with a PROTRACTOR. The measure of an angle can be any number between 0° and 180°. Angles can be labeled with numbers or letters. When angles are unknown, numbers can be used. When you want to formally call an angle you can identify it by three letters. Example Angle BCD would be an angle formed by Ray BC and Ray CD. Point C is the shared endpoint.

CLASSIFYING ANGLES Angles can be classified by their MEASURE. Protractors are used to find the EXACT angle measure. Once the Angle Measure is found, Angles fall into one of the following categories: ACUTE: An angle that measures between 0° and 90°. OBTUSE: An angle that measures between 90° and 180°. RIGHT: An angle that measures EXACTLY 90°. STRAIGHT: An angle that measures EXACTLY 180°

COMPLEMENTARY ANGLES When you have 2 angles that measure 90 degrees, they are referred to as being COMPLEMENTARY. Here, 2 small measure or ACUTE angles will combine to equal 90°. The BASIC formula to solve COMPLEMENTARY Angles is: Angle 1 + Angle 2 = 90°. Example: Two angles are COMPLEMENTARY, Angle 1 measures 34°. Please find the measure for the Angle 2. Angle 1 + Angle 2 = 90° -Here, the Basic Formula is used 34° + Angle 2 = 90° -Drop in the known Angle Measures -34° -34° -Solve Algebraically Angle 2 = 56° -Result is your answer

Finding MORE Complements Two angles are COMPLEMENTARY, Angle 1 measures 28°. Please find the measure for the Angle 2. Angle 1 + Angle 2 = 90° -Basic Formula is used 28° + Angle 2 = 90° -Drop in the known Angle Measures -28° -28° -Solve Algebraically Angle 2 = 62° -Result is your answer Two angles are COMPLEMENTARY, Angle 1 measures 35°. Please find the measure for the Angle 2. Angle 1 + Angle 2 = 90° -Basic Formula is used 35° + Angle 2 = 90° -Drop in the known Angle Measures -35° -35° -Solve Algebraically Angle 2 = 55° -Result is your answer

SUPPLEMENTARY ANGLES When you have 2 angles that measure 180 degrees(180°), they are referred to as being SUPPLEMENTARY. Here, 2 angles of any measure will combine to equal 180°. The BASIC formula to solve COMPLEMENTARY Angles is: Angle 1 + Angle 2 = 180°. Example: Two angles are SUPPLEMENTARY, Angle 1 measures 105°. Please find the measure for the Angle 2. Angle 1 + Angle 2 = 180° -Here, the Basic Formula is used 105° + Angle 2 = 180° -Drop in the known Angle Measures -105° -105° -Solve Algebraically Angle 2 = 75° -Result is your answer

Finding MORE Supplements Two angles are SUPPLEMENTARY, Angle 1 measures 85°. Please find the measure for the Angle 2. Angle 1 + Angle 2 = 180° -Basic Formula is used 85° + Angle 2 = 180° -Drop in the known Angle Measures -85° -85° -Solve Algebraically Angle 2 = 95° -Result is your answer Two angles are SUPPLEMENTARY, Angle 1 measures 114°. Please find the measure for the Angle 2. Angle 1 + Angle 2 = 180° -Basic Formula is used 114° + Angle 2 = 180° -Drop in the known Angle Measures -114° -114° -Solve Algebraically Angle 2 = 66° -Result is your answer

ADJACENT & VERTICAL ANGLES What are ADJACENT Angles? ADJACENT angles are Angles that sit right next to each other. They share a side and an endpoint. They BUTT up against each other. Think of them like BEST Friends who have to be near each other ALL the time. What are VERTICAL Angles? VERTICAL Angles are Angles that are OPPOSITE to each other. They are made from a pair of Intersecting lines and share a point. Some people think of them as MIRROR Images of each other.

QUICK REVIEW Classifying Angles: Finding Complements: There are 4 ways an Angle can be classified: ACUTE (Under 90°), OBTUSE (Over 90° but Under 180°), RIGHT (EXACTLY 90°), or STRAIGHT (EXACTLY 180°). Finding Complements: Angle 1 + Angle 2 = 90° Finding Supplements Angle 1 + Angle 2 = 180° Types of Angles Adjacent Angles: Angles that share a vertex & a side but no interior points. Vertical Angles: Angles formed by Intersecting Lines and are OPPOSITE from each other. Congruent Angles: Angles that possess the SAME measure.

Check for Understanding Please determine the BEST answer for the following expression. Carry out ALL work and calculations in your NOTES for later reference Please write your answer on your wipe boards and wait for the teacher’s signal. On the count of 3, hold up your wipe boards.

C4U Question #1 Question #1: Two angles are COMPLEMENTARY, Angle 1 measures 29°. Please find the measure for the Angle 2. Please work out the problem within your notes Write the correct answer on your wipe board. Wait for Teacher’s Signal.

C4U Question #2 Question #2: Two angles are COMPLEMENTARY, Angle 1 measures 61°. Please find the measure for the Angle 2. Please work out the problem within your notes Write the correct answer on your wipe board. Wait for Teacher’s Signal.

C4U Question #3 Question #3: Two angles are SUPPLEMENTARY, Angle 1 measures 41°. Please find the measure for the Angle 2. Please work out the problem within your notes Write the correct answer on your wipe board. Wait for Teacher’s Signal.

C4U Question #4 Question #4: Two angles are SUPPLEMENTARY, Angle 1 measures 73°. Please find the measure for the Angle 2. Please work out the problem within your notes Write the correct answer on your wipe board. Wait for Teacher’s Signal.

GUIDED PRACTICE Students will work on a worksheet/book work, focusing only on the problems assigned by the teacher. Work carefully, show your problem solving process, and double check all calculations. Use scratch paper to carry out your work. Once you have completed the assigned problems, please raise your pencil. The teacher will then check your work and release you to complete the independent practice.

INDEPENDENT PRACTICE Once you have been signed off and released to complete Independent Practice, please complete the following assignment: