Before Why is it important for the blade of a hockey stick to lie flat on the ice? What type of angle is formed by the 45 angle and the lie angle?

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1 Supplementary Angles LAUNCH (9 MIN) Before Why is it important for the blade of a hockey stick to lie flat on the ice? What type of angle is formed by the 45 angle and the lie angle? During How are the measures of the 45 angle and the lie angle related? Explain. After Some hockey players use sticks that are longer than normal because of their positions on the team. How will the lie angle be different for two players of the same height if one of the players uses a longer stick? KEY CONCEPT (4 MIN) Students learn the formal term, supplementary, for the relationship they discovered in the Launch. How are supplementary angles similar to complementary angles? How are they different? PART 1 (9 MIN) How do you expect each drawing to look when your sketch is complete? Dana Says (Screen 1) Use the Dana Says button to suggest that a piece of notebook paper might help students draw the supplementary angles, just as it helped them draw complementary angles in the previous lesson. How can part of a piece of paper help you draw a supplementary angle? While solving the problem How can you find the measure of each supplement? Which do you think is easier to draw adjacent complementary angles or adjacent supplementary angles? PART 2 (9 MIN) Have you seen a problem like this before? Explain. Dana Says (Screen 1) Use the Dana Says button to remind students of the relationship between adjacent supplementary angles. How can you use information from the diagram to solve the problem? Do two angles need to be adjacent to be supplementary? Explain. CLOSE AND CHECK (9 MIN) When would you describe the relationship between two angles as supplementary? Why is it useful to know that two angles are supplementary? What is an example of a situation in which two angles are supplementary but not adjacent?

2 Supplementary Angles LESSON OBJECTIVES 1. Use facts about supplementary angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. 2. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. FOCUS QUESTION What do you know about the measures of two angles that form a straight angle? MATH BACKGROUND In the previous lesson, students saw that two angles are complementary if the sum of their measures is 90. In this lesson, they learn that there is also a special name for two angles whose measures add up to 180 The skills students develop for working with supplementary angles are similar to those they learned for complementary angles. In particular, they draw adjacent supplements for given angles and find the measures of the supplements. They also write algebraic equations to model supplementary angle relationships, and solve the equations to find unknown values. In the next lesson, students use their knowledge of supplementary angles to draw important conclusions about another type of angle pair called vertical angles. Supplementary angles will also be used in future math courses to prove results about triangles, parallelograms, parallel lines, and other geometric objects. LAUNCH (9 MIN) Objective: Use facts about supplementary angles to solve a real-world problem. Author Intent Students apply what they know about measures of straight angles and adjacent angles to solve a problem. Based on their study of complementary angles, students may recognize that a special relationship exists between two angles whose combined measure is 180, although they will not learn the term supplementary until later in the lesson. Before Why is it important for the blade of a hockey stick to lie flat on the ice? [Sample answer: This makes it easier to stop, move, and shoot the puck.] What type of angle is formed by the 45 angle and the lie angle? [a straight angle] During How are the measures of the 45 angle and the lie angle related? Explain. [Sample answer: The sum of the measures of the angles is 180.] After Some hockey players use sticks that are longer than normal because of their positions on the team. How will the lie angle be different for two players of the same height if one of the players uses a longer stick? [Sample answer: The player with the longer stick will need a greater lie angle to ensure that the blade lies flat on the ice.]

3 Solution Notes The provided solution explains that since the lie angle and the 45 angle form a straight angle, the lie angle s measure is Students might also solve the problem by noting that the lie angle can be decomposed into a right angle and a complement of the 45 angle. So the lie angle s measure can also be expressed as , which simplifies to the same answer of 135. Connect Your Learning Move to the Connect Your Learning screen. Start a conversation about the problem in the Launch, focusing on how the 45 angle and the lie angle formed a straight angle. Discuss what this implies about the measures of the two angles. Draw other diagrams showing different adjacent angles that form straight angles. Students should recognize that although the measures of the adjacent angles may change, the sum of the measures is always 180. This understanding prepares them for the upcoming definition of supplementary angles in the Key Concept. KEY CONCEPT (4 MIN) ELL Support Beginning Play the video animation through once. Then play it again, pausing to examine the math each time the angle is changed. Call students attention to the v button at the bottom of the Key Concept screen and click on it. Have students read the definition of supplementary angles and remind them that they can refer to this definition as they move through the rest of the lesson. Using these linguistic supports should prepare students to read and answer a problem set like Part 1. Intermediate Complete the activity for beginning learners. Then have students summarize the information by making a flowchart that indicates how to find the adjacent supplementary angle in a pair of angles. [Sample: Students might write find angle measure from picture in the first bubble, subtract angle measure from 180 in the second bubble, and get the missing angle measure in the third bubble.] Students can use this flowchart to help them read and answer a problem set like Part 1. Advanced Complete the activity for beginning learners. Then have students write a sequenced set of instructions for finding supplementary angles that they can use in their later work solving problems. [Sample: To find the supplementary angle of a given angle, subtract the given angle measure from 180 degrees.] Teaching Tips for the Key Concept Students learn the formal term, supplementary, for the relationship they discovered in the Launch. Stress that angles may be supplementary even if they are not adjacent; what makes two angles supplementary is the fact that their measures sum to 180. How are supplementary angles similar to complementary angles? How are they different? [Sample answer: Like complementary angles, supplementary angles are two angles whose measures always add up to the same number. The measures of complementary angles add up to 90, whereas the measures of supplementary angles add up to 180.]

4 PART 1 (9 MIN) Objective: Draw (freehand or with ruler) adjacent supplementary angles. Author Intent In the previous lesson, students drew adjacent complements of angles and found their measures. Here they do the same thing with adjacent supplements. Students gain a deeper understanding of supplementary relationships and develop creative problemsolving skills by drawing supplements without a measuring device. Instructional Design Call three students to the whiteboard. Have each student draw an adjacent supplement for one of the given angles and then find the supplement s measure. To draw the supplement, the students can use a real-world object with a straight angle, such as a piece of notebook paper, or they can approximate the supplement based on their knowledge of what a straight angle looks like. How do you expect each drawing to look when your sketch is complete? [Sample answer: There will be three angles in the final sketch: the original angle, its supplement, and a straight angle formed by both.] Dana Says (Screen 1) Use the Dana Says button to suggest that a piece of notebook paper might help students draw the supplementary angles, just as it helped them draw complementary angles in the previous lesson. How can part of a piece of paper help you draw a supplementary angle? [Sample answer: Any edge of the paper can represent a straight angle. By using the edge to trace along one of the given angle s rays in the opposite direction, you can draw the adjacent supplement.] While solving the problem How can you find the measure of each supplement? [You can subtract the measure of the given angle from 180.] Which do you think is easier to draw adjacent complementary angles or adjacent supplementary angles? [Sample answer: I think drawing adjacent supplementary angles is easier because you just need to draw a straight line in order to form a straight angle and complete the supplement.] Solution Notes Students can use either of the rays in each given angle to form a straight angle and complete the adjacent supplement. So there are two possible supplements that can be drawn for each angle. You can ask students to draw both supplements if time permits. Differentiated Instruction For struggling students: Students may need help distinguishing between complementary and supplementary, since both terms are applied to pairs of angles whose measures always add up to the same number. Encourage students to develop a mnemonic device for remembering which is which. For example, the c in complementary could remind them of the c in corner, which has a 90 angle. Similarly, the s in supplementary could remind them of the s in straight angle. Another way to remember the difference is that c comes before s in the alphabet, so the sum of complementary angle measures (90 ) comes before the sum of supplementary angle measures (180 ).

5 For advanced students: Have students make problems that include both complementary and supplementary angles. Label one angle x and provide the clues needed to solve for x. Let students trade problems with a partner and solve each other s problems. Got It Notes Like the Example, the Got It gives the measure of an angle and asks students to find the measure of its supplement. However, this time the angle measure is a decimal. It may be helpful to review subtracting with decimals before presenting the problem. If you show answer choices, consider the following possible student errors: Students who choose A are mistakenly assuming that an angle and its supplement have the same measure. Students who choose B are finding the measure of the complement instead of the supplement. PART 2 (9 MIN) Objective: Use facts about supplementary angles to write and solve simple equations. Author Intent Students apply what they know about adjacent supplementary angles to write and solve an equation and find an unknown value. Students once again see the usefulness of algebra in solving geometric problems. Have you seen a problem like this before? Explain. [Sample answer: Yes; the problem is similar to the hockey problem in the Launch. In both problems you are given adjacent angles that form a straight angle. Also, in both problems you know the measure of one adjacent angle but not the other.] Dana Says (Screen 1) Use the Dana Says button to remind students of the relationship between adjacent supplementary angles. How can you use information from the diagram to solve the problem? [Sample answer: You can write an equation showing that the sum of the measures of the two angles is 180.] Do two angles need to be adjacent to be supplementary? Explain. [No; the term supplementary describes how the measures of the angles are related, not how the angles are located with respect to each other. As long as their measures add up to 180, they are supplementary.] Solution Notes The animated solution explains the reasoning behind each step while showing students the standard order of applying inverse operations to solve the equation (in this case, subtracting before dividing). You could also solve the equation by dividing first, as shown below, to remind students that there is often more than one way to solve a problem.

6 Got It Notes 2x x x x x 65 If you show answer choices, consider the following possible student errors: Students who choose A may have mistakenly thought that the two angles must have the same measure. Students who choose D have found the measure of the unknown angle, 4x, instead of the value of x. Got It 2 Notes Some students may solve this problem mentally by reasoning that , which is the measure of a right angle. Other students may find it helpful to use an equation. They can let x be the measure of one of the supplementary angles and then solve the equation x x 180. CLOSE AND CHECK (9 MIN) Focus Question Sample Answer Two angles that form a straight angle are called supplementary angles. Since a straight angle measures 180, the sum of the measures of the two angles is also 180. Focus Question Notes Make sure students understand that not all supplementary angles are adjacent, so they may not look like they can form a straight angle. Also, emphasize that if two angles are supplementary and you know the measure of one of them, you can always find the measure of the other angle by subtracting the known measure from 180. Essential Question Connection This lesson addresses the Essential Question about how you can best describe relationships between angles and whether some relationships are more useful than others. Use the following questions to help students connect this lesson to the Essential Question. When would you describe the relationship between two angles as supplementary? [I would describe the relationship as supplementary if the sum of the measures of the angles is 180.] Why is it useful to know that two angles are supplementary? [Sample answer: If you know the measure of one of the angles, you can subtract the known measure from 180 to find the measure of the other angle.] What is an example of a situation in which two angles are supplementary but not adjacent? [Sample Answer: The angles formed by two corners of a piece of paper are supplementary because they are right angles, and However, the angles are not adjacent because they do not share a vertex.]