Angles Formed by Intersecting Lines

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1 1 3 Locker LESSON 19.1 Angles Formed by Intersecting Lines Common Core Math Standards The student is expected to: G-CO.9 Prove theorems about lines and angles. Mathematical Practices MP.3 Logic Name Class Date 19.1 Angles Formed by Intersecting Lines Essential Question: How can you find the measures of angles formed by intersecting lines? Explore 1 Exploring Angle Pairs Formed by Intersecting Lines When two lines intersect, like the blades of a pair of scissors, a number of angle pairs are formed. You can find relationships between the measures of the angles in each pair. Resource Locker Language Objective Explain to a partner the differences among complementary angles, supplementary angles, linear pairs, and vertical angles. ENGAGE Essential Question: How can you find the measures of angles formed by intersecting lines? Possible answer: Identify any angles with known angle measures. Look for pairs of vertical angles and linear pairs of angles. Find angles that are complementary (if any) and supplementary. Use these relationships between pairs of angles together with the known angle measures to find the missing measures. PREVIEW: LESSON PERFORMANCE TASK View the Engage section online. Discuss the photo, making sure students understand that a multiplying effect is created by the long handle and the short jaws. Then preview the Lesson Performance Task. Image Credits: MNI/ Shutterstock A B Using a straightedge, draw a pair of intersecting lines like the open scissors. Label the angles formed as 1, 2, 3, and 4. Possible answer: Use a protractor to find each measure. Angle m 1 m 2 m 3 m 4 m 1 + m 2 m 2 + m 3 m 3 + m 4 m 1 + m 4 Measure of Angle Module Lesson 1 Name Class Date 19.1 Angles Formed by Intersecting Lines Essential Question: How can you find the measures of angles formed by intersecting lines? G-CO.9 Prove theorems about lines and angles. Image Credits: MNI/ Shutterstock Explore 1 Exploring Angle Pairs Formed by Intersecting Lines When two lines intersect, like the blades of a pair of scissors, a number of angle pairs are formed. You can find relationships between the measures of the angles in each pair. Using a straightedge, draw a pair of intersecting lines like the open scissors. Label the angles formed as 1, 2, 3, and 4. Possible answer: 4 2 Use a protractor to find each measure. Angle Measure of Angle m 1 m 2 m 3 m 4 m 1 + m 2 m 2 + m 3 m 3 + m 4 m 1 + m 4 Resource HARDCOVER PAGES Turn to these pages to find this lesson in the hardcover student edition. Module Lesson Lesson 19.1

2 You have been measuring vertical angles and linear pairs of angles. When two lines intersect, the angles that are opposite each other are vertical angles. Recall that a linear pair is a pair of adjacent angles whose non-common sides are opposite rays. So, when two lines intersect, the angles that are on the same side of a line form a linear pair. Reflect 1. Name a pair of vertical angles and a linear pair of angles in your diagram in Step A. Possible answers: vertical angles: 1 and 3 or 2 and 4 ; linear pairs: 1 and 2, 2 and 3, 3 and 4, or 1 and 4 2. Make a conjecture about the measures of a pair of vertical angles. Vertical angles have the same measure and so are congruent. 3. Use the Linear Pair Theorem to tell what you know about the measures of angles that form a linear pair. The angles in a linear pair are supplementary, so the measures of the angles add up to. Explore 2 Proving the Vertical Angles Theorem The conjecture from the Explore about vertical angles can be proven so it can be stated as a theorem. The Vertical Angles Theorem If two angles are vertical angles, then the angles are congruent EXPLORE 1 Exploring Angle Pairs Formed by Intersecting Lines INTEGRATE TECHNOLOGY Students have the option of exploring the activity either in the book or online. QUESTIONING STRATEGIES How would you describe a pair of supplementary angles in the drawing of intersecting lines? adjacent angles Which pair of angles, if any, are congruent in a drawing of two intersecting lines? Opposite angles are congruent. 1 3 and 2 4 You have written proofs in two-column and paragraph proof formats. Another type of proof is called a flow proof. A flow proof uses boxes and arrows to show the structure of the proof. The steps in a flow proof move from left to right or from top to bottom, shown by the arrows connecting each box. The justification for each step is written below the box. You can use a flow proof to prove the Vertical Angles Theorem. Follow the steps to write a Plan for Proof and a flow proof to prove the Vertical Angles Theorem. Given: 1 and 3 are vertical angles. Prove: EXPLORE 2 Proving the Vertical Angles Theorem QUESTIONING STRATEGIES How do you identify vertical angles? They are opposite angles formed by intersecting lines. Module Lesson 1 PROFESSIONAL DEVELOPMENT Math Background Students will work with special angles. Congruent angles have the same measure. A pair of angles is supplementary if their sum is. A pair of angles is complementary if their sum is 90. Adjacent angles share one side without overlapping. Vertical angles are the non-adjacent angles formed by intersecting lines. They lie opposite each other at the point of intersection. Angles Formed by Intersecting Lines 934

3 AVOID COMMON ERRORS A common error that students make in writing proofs is using the result they are trying to prove as an intermediate step in the proof. Remind students to be alert for this type of circular reasoning. CURRICULUM INTEGRATION The common error mentioned above is discussed in the study of logic; it is known as the logical fallacy of begging the question. This is not the same as the general use of the phrase to beg the question, which often means to raise another question. A B Complete the final steps of a Plan for Proof: Because 1 and 2 are a linear pair and 2 and 3 are a linear pair, these pairs of angles are supplementary. This means that m 1 + m 2 = and m 2 + m 3 =. By the Transitive Property, m 1 + m 2 = m 2 + m 3. Next: Subtract m 2 from both sides to conclude that m 1 = m 3. So, 1 3. Use the Plan for Proof to complete the flow proof. Begin with what you know is true from the Given or the diagram. Use arrows to show the path of the reasoning. Fill in the missing statement or reason in each step. 1 and 2 are a linear pair. Given (see diagram) 1 and 3 are vertical angles. Given 2 and 3 are a linear pair. Given (see diagram) 1 and 2 are supplementary. Linear Pair Theorem 2 and 3 are supplementary. Linear Pair Theorem m 1 + m 2 = Def. of supplementary angles m 2 + m 3 = Def. of supplementary angles 1 3 m 1 = m 3 m 1 + m 2 = m 2 + m 3 Def. of congruence Subtraction Property of Equality Transitive Property of Equality Reflect 4. Discussion Using the other pair of angles in the diagram, 2 and 4, would a proof that 2 4 also show that the Vertical Angles Theorem is true? Explain why or why not. Yes, it does not matter which pair of vertical angles is used in the proof. Similar statements and reasons could be used for either pair of vertical angles. 5. Draw two intersecting lines to form vertical angles. Label your lines and tell which angles are congruent. Measure the angles to check that they are congruent. A D E Possible answer: C B By the Vertical Angles Theorem, AEC DEB and AED CEB. Checking by measuring, m AEC = m DEB = 45 and m AED = m CEB = 135. Module Lesson Lesson 19.1 COLLABORATIVE LEARNING Small Group Activity Have students review the different angle pairs and lesson illustrations. Have each student draw one example of an angle pair, choosing from: a linear pair, supplementary angles, complementary angles, and vertical angles. Students then pass their drawings to others, who list all the information they know about that type of angle pair. Have them keep passing the drawings for other students to add more information until the drawing comes back to the student who drew it. Then have students identify and draw the angle that is a complement of an acute angle, a supplement of an obtuse angle, and the supplement of a right angle. acute, acute, right

4 Explain 1 Using Vertical Angles You can use the Vertical Angles Theorem to find missing angle measures in situations involving intersecting lines. Example 1 Cross braces help keep the deck posts straight. Find the measure of each angle. EXPLAIN 1 Using Vertical Angles QUESTIONING STRATEGIES 6 Because vertical angles are congruent, m 6 = If two lines intersect to form four angles and one angle is an 80-degree angle, how do you know there is another 80-degree angle? The 80-degree angle forms a linear pair with two 100-degree angles, and they each form a linear pair with the remaining angle, so that angle must measure 80 degrees. 5 and 7 From Part A, m 6 = 146. Because 5 and 6 form a, they are supplementary and m 5 = = 34. m 7 = 34 because 7 also forms a linear pair with 6, or because it is a vertical angle with 5. Your Turn linear pair 6. The measures of two vertical angles are 58 and (3x + 4). Find the value of x. 58 = 3x = 3x 18 = x 7. The measures of two vertical angles are given by the expressions (x + 3) and (2x - 7). Find the value of x. What is the measure of each angle? x + 3 = 2x - 7 x + 10 = 2x 10 = x The measure of each angle is (x + 3) = (10 + 3) = 13. CONNECT VOCABULARY Differentiate the word vertical, meaning up and down, and the idea of vertical angles, which share a vertex but don t need to be in an up-and-down position. They are vertical in respect to one another. Module Lesson 1 DIFFERENTIATE INSTRUCTION Graphic Organizers Have students create a graphic organizer with a central oval titled Pairs of Angles with leader lines to boxes for Adjacent angles, Linear pairs, Vertical angles, Supplementary angles, and Complementary angles. Ask students to draw and label an example of each pair of angles and to write a definition of each type of angle pair. Angles Formed by Intersecting Lines 936

5 EXPLAIN 2 Using Supplementary and Complementary Angles Explain 2 Using Supplementary and Complementary Angles Recall what you know about complementary and supplementary angles. Complementary angles are two angles whose measures have a sum of 90. Supplementary angles are two angles whose measures have a sum of. You have seen that two angles that form a linear pair are supplementary. Example 2 Use the diagram below to find the missing angle measures. Explain your reasoning. INTEGRATE MATHEMATICAL Focus on Critical Thinking MP.3 Ask students what the maximum size of a supplementary angle might be. Encourage students to state that the angle measure is close to, but not exactly,. Have them try to describe two lines that intersect to form these angles. QUESTIONING STRATEGIES What fact do you use to find the angle measures in a linear pair? The angles in a linear pair are supplementary. What fact do you use to find the angle measures in a pair of complementary angles? Two angles are complementary if the sum of their measures is 90. How does an angle complementary to an angle A compare with an angle supplementary to A? It measures 90 less. INTEGRATE MATHEMATICAL Focus on Reasoning MP.2 Encourage students to write an equation to solve for the measure of an angle in an angle-pair relationship.students will write an equation to represent the angle-pair relationship and substitute the information that they are given to solve for the unknown. CONNECT VOCABULARY To help students remember the definitions of complementary and supplementary, explain that the letter c for complementary comes before s for supplementary, just as 90 comes before. 937 Lesson 19.1 B A Find the measures of AFC and AFB. AFC and CFD are a linear pair formed by an intersecting line and ray, AD and FC, so they are supplementary and the sum of their measures is. By the diagram, m CFD = 90, so m AFC = - 90 = 90 and AFC is also a right angle. Because together they form the right angle AFC, AFB and BFC are complementary and the sum of their measures is 90. So, m AFB = 90 - m BFC = = 40. Find the measures of DFE and AFE. BFA and DFE are formed by two intersecting lines and are opposite each other, so the angles are vertical angles. So, the angles are congruent. From Part A m AFB = 40, so m DFE = also. Because BFA and AFE form a linear pair, the angles are supplementary and the sum of their measures is. So, m AFE = - m BFA = - 40 = 140. Reflect C 50 F D E In Part A, what do you notice about right angles AFC and CFD? Make a conjecture about right angles. Possible answer: Both angles have measure 90. Conjecture: All right angles are congruent. Module Lesson 1 LANGUAGE SUPPORT Visual Cues Have students work in pairs to fill out an organizer like the following, starting with prior knowledge: Angle(s) Definition Picture Right Obtuse Acute Complementary Supplementary

6 Your Turn You can represent the measures of an angle and its complement as x and (90 - x). Similarly, you can represent the measures of an angle and its supplement as x and (180 - x). Use these expressions to find the measures of the angles described. 9. The measure of an angle is equal to the measure of its complement. x = 90 - x 2x = 90 x = 45; so, 90 - x = 45 The measure of the angle is 45 the measure of its complement is 45. Elaborate 10. The measure of an angle is twice the measure of its supplement. x = 2 (180 - x) x = 360-2x 3x = 360 x = 120; so, x = 60 The measure of the angle is 120 the measure of its supplement is Describe how proving a theorem is different than solving a problem and describe how they are the same. Possible answer: A theorem is a general statement and can be used to justify steps in solving problems, which are specific cases of algebraic and geometric relationships. Both proofs and problem solving use a logical sequence of steps to justify a conclusion or to find a solution. 12. Discussion The proof of the Vertical Angles Theorem in the lesson includes a Plan for Proof. How are a Plan for Proof and the proof itself the same and how are they different? Possible answer: A plan for a proof is less formal than a proof. Both start from the given information and reach the final conclusion, but a formal proof presents every logical step in detail, while a plan describes only the key logical steps. 13. Draw two intersecting lines. Label points on the lines and tell what angles you know are congruent and which are supplementary. Possible answer: Vertical angles are congruent: GLK JLH and GLJ KLH Angles in a linear pair are supplementary: GLJ and GLK; GLJ and JLH; JLH and HLK; and HLK and GLK 14. Essential Question Check-In If you know that the measure of one angle in a linear pair is 75, how can you find the measure of the other angle? The angles in a linear pair are supplementary, so subtract the known measure from : = 105, so the measure of the other angle is 105. G J L K H ELABORATE INTEGRATE MATHEMATICAL Focus on Technology MP.5 You may want to have students explore the theorems in this lesson using geometry software. For example, have students construct a linear pair of angles, determine the measure of each angle, and use the software s calculate tool to find the sum of the measures. Students can change the size of the angles and see that the measures change while their sum remains constant. QUESTIONING STRATEGIES How many vertical angle pairs are formed where three lines intersect at a point? Explain. 6; if the small angles are numberered consecutively 1 6, the vertical angles are 1 and 4, 2 and 5, 3 and 6, and the adjacent angle pairs 1 2 and 4 5, 2 3 and 5 6, 3 4, and 6 1. SUMMARIZE THE LESSON Have students make a graphic organizer to show how some of the properties, postulates, and theorems in this lesson build upon one another. A sample is shown below. Angle Addition Postulate Linear Pair Theorem Module Lesson 1 Vertical Angles Theorem Angles Formed by Intersecting Lines 938

7 EVALUATE Evaluate: Homework and Practice Use this diagram and information for Exercises 1 4. Given: m AFB = m EFD = 50 Online Homework Hints and Help Extra Practice ASSIGNMENT GUIDE Points B, F, D and points E, F, C are collinear. A E B F C D Concepts and Skills Explore Exploring Angle Pairs Formed by Intersecting Lines Example 1 Proving the Vertical Angles Theorem Example 2 Using Supplementary and Complementary Angles CONNECT VOCABULARY Practice Exercise 1 Exercises 2 11 Exercises Suggest still another way for students to remember which sum is 90 and which is 180: complementary and corner both start with the letter c, and corners are often right angles. Supplementary and straight both start with the letter s, and a straight line is a angle. Image Credits: Fresh Picked/Alamy 1. Determine whether each pair of angles is a pair of vertical angles, a linear pair of angles, or neither. Select the correct answer for each lettered part. A. BFC and DFE Vertical Linear Pair Neither B. BFA and DFE Vertical Linear Pair Neither C. BFC and CFD Vertical Linear Pair Neither D. AFE and AFC Vertical Linear Pair Neither E. BFE and CFD Vertical Linear Pair Neither F. AFE and BFC Vertical Linear Pair Neither 2. Find m AFE. 3. Find m DFC. m AFB + m AFE + m EFD = 50 + m AFE + 50 = m AFE = Find m BFC. m BFC = m EFD = Represent Real-World Problems A sprinkler swings back and forth between A and B in such a way that 1 2, 1 and 3 are complementary, and 2 and 4 are complementary. If m 1 = 47.5, find m 2, m 3, and m , so m 2 = 47.5 A and 3 are complementary, so m 3 = = and 4 are complementary, so m 4 = =42.5 B m EFB = m AFB + m AFE = = 130 m DFC = m EFB, so m DFC = 130 Module Lesson 1 Exercise Depth of Knowledge (D.O.K.) Mathematical Practices 1 1 Recall of Information MP.4 Modeling Recall of Information MP.2 Reasoning Skills/Concepts MP.2 Reasoning Recall of Information MP.3 Logic Skills/Concepts MP.3 Logic 15 2 Skills/Concepts MP.4 Modeling 939 Lesson 19.1

8 Determine whether each statement is true or false. If false, explain why. 6. If an angle is acute, then the measure of its complement must be greater than the measure of its supplement. False. The measure of an acute angle is less than 90, so the measure of its complement will be less than 90 and the measure of its supplement will be greater than 90. So, the measure of the supplement will be greater than the measure of the complement. 7. A pair of vertical angles may also form a linear pair. False. Vertical angles do not share a common side. 8. If two angles are supplementary and congruent, the measure of each angle is 90. True 9. If a ray divides an angle into two complementary angles, then the original angle is a right angle. True You can represent the measures of an angle and its complement as x and (90 - x). Similarly, you can represent the measures of an angle and its supplement as x and (180 - x). Use these expressions to find the measures of the angles described. 10. The measure of an angle is three times the measure of its supplement. x = 3 (180 - x) x = 540-3x 4x = 540 x = 135; so, x = 45 The measure of the angle is 135 and the measure of its supplement is The measure of the supplement of an angle is three times the measure of its complement x = 3 (90 - x) x = 270-3x 2x = 90 x = 45; so, 90 - x = 45 and x = 135 The measure of the angle is 45, the measure of its complement is 45, and the measure of its supplement is The measure of an angle increased by 20 is equal to the measure of its complement. x + 20 = 90 - x 2x = 70 x = 35; so, 90 - x = 55 The measure of the angle is 35, the measure of its complement is 55. INTEGRATE MATHEMATICAL Focus on Communication MP.3 As students answer the questions using the angle names in a pair of angles, encourage them to trace each angle along its letters and say the angle s name aloud as they write it. This will help students get used to naming an angle with three letters. AVOID COMMON ERRORS Some students may have difficulty organizing the reasons or steps for a proof. You may wish to have students write the given reasons or steps on sticky notes. Then they can rearrange the sticky notes as needed to write the proof in the correct order. Module Lesson 1 Exercise Depth of Knowledge (D.O.K.) Mathematical Practices Strategic Thinking MP.2 Reasoning Strategic Thinking MP.3 Logic Angles Formed by Intersecting Lines 940

9 INTEGRATE MATHEMATICAL Focus on Modeling MP.4 Remind students that the shape of the letter X suggests the idea of vertical angles. INTEGRATE MATHEMATICAL Focus on Math Connections MP.1 Remind students of the definitions of vertical, complementary, supplementary, and linear pairs. Have students use mental math to find complements and supplements of angles before using variables or expressions. Write a plan for a proof for each theorem. 13. If two angles are congruent, then their complements are congruent. Given: ABC DEF Prove: The complement of ABC the complement of DEF. Plan for Proof: If ABC DEF, then m ABC = m DEF. The measure of the complement of ABC = 90 - m ABC. The measure of the complement of DEF = 90 - m DEF. Since m ABC = m DEF, the measure of the complement of DEF = 90 - m ABC. Therefore, the measure of the complement of ABC = the measure of the complements of DEF. The measures of the complements of the angles are equal, so the complements of the angles are congruent. 14. If two angles are congruent, then their supplements are congruent. Given: ABC DEF Prove: The supplement of ABC the supplement of DEF. Plan for Proof: If ABC DEF, then m ABC m DEF. The measure of the supplement of ABC = - m ABC. The measure of the supplement of DEF = - m DEF. Since m ABC = m DEF, the measure of the supplement of DEF = - m ABC. Therefore, the measure of the supplement of ABC = the measure of the supplement of DEF. The measures of the supplements of the angles are equal, so the supplements of the angles are congruent. Module Lesson Lesson 19.1

10 15. Justify Reasoning Complete the two-column proof for the theorem If two angles are congruent, then their supplements are congruent. Statements 1. ABC DEF 1. Given 2. The measure of the supplement of ABC = - m ABC. 3. The measure of the supplement of DEF = - m DEF. m ABC = m DEF 4. Reasons supplement 2. Definition of the of an angle 3. Definition of the supplement of an angle 4. If two angles are congruent, their measures are equal. INTEGRATE MATHEMATICAL Focus on Critical Thinking MP.3 If students have difficulty supplying the missing reasons in a proof, give them the reasons in random order and ask them to write the correct reason in the appropriate line of the proof. This type of scaffolding can be helpful for English language learners until they become more comfortable with the vocabulary of deductive reasoning. 5. The measure of the supplement of DEF = - m ABC. 5. Substitution Property of Equality 6. The measure of the supplement of ABC = the measure of the supplement of DEF. 7. The supplement of ABC the supplement of DEF. Substitution Property of Equality If the measures of the supplements of two angles are equal, then supplements of the angles are congruent. 16. Probability The probability P of choosing an object at random from a group of objects is found by the fraction P(event) = Number of favorable outcomes. Suppose the angle measures 30, 60, 120, and 150 Total number of outcomes are written on slips of paper. You choose two slips of paper at random. a. What is the probability that the measures you choose are complementary? 1 possible pair (30, 60 ) P(complementary) = = 1_ 6 angle pairs total 6 b. What is the probability that the measures you choose are supplementary? 2 possible pairs (30, 150 and 60, 120 ) P(supplementary) = = 2_ 6 angle pairs total 6 = 1_ 3 Module Lesson 1 Angles Formed by Intersecting Lines 942

11 PEER-TO-PEER DISCUSSION Ask students to discuss with a partner the names and diagrams for various pairs of angles introduced in this lesson. Ask them to write and solve a word problem using complementary or supplementary angles on index cards, then switch cards with their partners to solve the problem. JOURNAL Have students write about each angle-pair relationship discussed in this lesson (supplementary angles, complementary angles, and vertical angles). Students should include definitions and drawings to support their descriptions. H.O.T. Focus on Higher Order Thinking 17. Communicate Mathematical Ideas Write a proof of the Vertical Angles Theorem in paragraph proof form. Given: 2 and 4 are vertical angles. 4 Prove: 2 4 In the diagram of intersecting lines, 2 and 4 are vertical angles. Also, 2 and 3 are a linear pair and 3 and 4 are a linear pair. By the Linear Pair Theorem, 2 and 3 are supplementary and 3 and 4 are supplementary. Then m 2 + m 3 = and m 3 + m 4 = by the definition of supplementary angles. By the Transitive Property of Equality, m 2 + m 3 = m 3 + m 4. Using the Subtraction Property of Equality, m 2 = m 4. So, 2 4 by the definition of congruence. 18. Analyze Relationships If one angle of a linear pair is acute, then the other angle must be obtuse. Explain why. 1 3 The sum of the measures of the two angles of a linear pair must be. If the measure of one angle is less than 90, then the measure of the other angle must be greater than Critique Reasoning Your friend says that there is an angle whose measure is the same as the measure of the sum of its supplement and its complement. Is your friend correct? What is the measure of the angle? Explain your friend s reasoning. Yes; 90 : the measure of its complement is 0, and the measure of its supplement is 90, so = Critical Thinking Two statements in a proof are: m A = m B m B = m C What reason could you give for the statement m A = m C? Explain your reasoning. You could use either the Transitive Property of Equality, since both statements have m B in common; or you could use the Substitution Property of Equality by substituting m C for m B in the first statement. Module Lesson Lesson 19.1

12 Lesson Performance Task The image shows the angles formed by a pair of scissors. When the scissors are closed, m 1 = 0. As the scissors are opened, the measures of all four angles change in relation to each other. Describe how the measures change as m 1 increases from 0 to. When m 1 = 0, m 3 = 0, and the measures of both 2 and 4 equal. As m 1 increases, the measure of 3 increases as well, so that m 3 always equals m 1. At the same time, the measures of 2 and 4 decrease steadily, both angles being congruent to each other and supplementary to 1. When m 1 = 90, the measures of the other three angles are also 90. When m 1 > 90, the measures of 2 and 4 are less than 90 and continually decrease, reaching 0 when m 1 = CONNECT VOCABULARY A supplement is something that completes something else, as a vitamin supplement may complete a person s daily vitamin requirement. The supplement of an angle completes a linear pair, with measures that complete a sum of. A complement similarly brings something to completion, like a new coach who proves to be a perfect complement to the team. The complement of an angle brings a right angle to completion. AVOID COMMON ERRORS Students may have difficulty with the concept that as angle measures increase from 0 to, their supplements change from obtuse to right to acute angles. Stress that supplementary angles have measures whose sum is, and that one angle in a pair of supplementary angles that are not right angles will always be obtuse and one will be acute, and that supplements of right angles are right angles. Module Lesson 1 EXTENSION ACTIVITY A lever is a simple machine that enables the user to lift or move an object using less force than the weight of the object. A teeter-totter is an example of a class 1 lever, which has a fulcrum between the object being moved and the applied force. Have students research double class 1 levers, of which pliers and scissors are examples. Students should explain how this type of lever differs from single class 1 levers, and describe how double class 1 levers create a mechanical advantage that allows users to produce forces greater than they apply. Class 1 Lever Load Fulcrum Force Scoring Rubric 2 points: Student correctly solves the problem and explains his/her reasoning. 1 point: Student shows good understanding of the problem but does not fully solve or explain his/her reasoning. 0 points: Student does not demonstrate understanding of the problem. Angles Formed by Intersecting Lines 944

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