Math CC 7: Shapes & Designs Inv. 2 Name: Per:

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1 Math CC 7: Shapes & Designs Inv. 2 Name: Per: Day 1 Friday 10/27 Day 2 Monday 10/30 Day 3 Tuesday 10/31 Day 4 Wednesday 11/1 Day 5 Thursday 11/2 Day 6 Friday 11/3 SHAPES & DESIGNS-Inv. 2: DESIGNING POLYGONS: THE ANGLE CONNECTION Learning Target/s Classwork Homework Self-Assess Learning I can find a missing angle in a triangle. I can identify what side lengths make a triangle. I can draw triangles with specific criteria. I can solve simple two step equations I can find missing angles based on angle relationships (complementary, supplementary, and vertical). Pg. 2-3 SD Interior Angle Sums, and finding Missing Angles in Triangles Pg. 6 SD 3.1: Building Triangles Pg. 8 SD 3.2 Design Challenge Pg. 9 Two-step equations Pg SD 3.4: Vertical Angles Pg Practice with All Angle Relationships Please check skyward: My current math grade is For the Shapes and Designs Unit I have missing assignments Day 1 p. 4 Complete and correct with online EDPUZZLE Day 2: p. 7 Edpuzzle: two-step equation pre-teach Take the night off! Enjoy whatever you want to celebrate! Day 4 p.11 Complete and CORRECT with the EDpuzzle Day 5 p.14 Complete and CORRECT with the EDpuzzle Day 5: p. 17 Complete and correct with EDPuzzle Days 7: 11/6- Unit review Day 8: 11/7-Google Document Day 9: 11/8-Unit Test SD 7.G.2: Draw, with ruler and protractor, triangles with given conditions. Investigatio 7.G.2: Identify when the conditions determine a unique triangle, more than one n 2 triangle or no triangle. Common Core Standards 7.G.5: Use facts about supplementary, complementary, vertical, and adjacent angles to write and solve simple equations for an unknown angle in a figure. I have reviewed with a parent/guardian and I am satisfied with the work produced in this packet. Student Signature: Parent/Guardian Signature: Date: 1

2 Day 1: SD : Interior Angle Sum of a Triangle. Finding Missing Angles in Triangles Measure the interior angles in each triangle and find the sum. Triangle 1 Angle 1 Angle 2 Angle 3 Write and Solve An Equation to find the Sum of the Angles = What is the sum of the interior angles in any triangle? If you know the sum of the interior angles of a triangle is always, then you can solve for a missing angle in a triangle. 2

3 A. For each of the triangles below, write and solve an equation to find the value of the unknown angle. Use the results to find the size of each angle. B. For each of the triangles below, write and solve an equation to find the value of x and then find the size of each angle. Equation: Equation: Challenge (optional): 3

4 Day 1: SD HOMEWORK. Correct with EdPuzzle Find the missing angle in each of the triangles below. Make sure that you write an equation for each problem. Equation: Equation: Equation: Angle: Angle: Angle: Find the missing angle in each of the angle relationships below. Make sure that you write an equation for each problem These two angles are (Circle one): These two angles are (Circle one): These two angles are (Circle one): Complementary/Supplementary Complementary/Supplementary Complementary/Supplementary Equation: Equation: Equation: Angle x= Angle x= Angle x= These two angles are (Circle one): These two angles are (Circle one): These two angles are (Circle one): Complementary/Supplementary Complementary/Supplementary Complementary/Supplementary Equation: Equation: Equation: Angle x= Angle x= Angle x= 4

5 Day 2: SD 3.1: Building Triangles A. Try to make a triangle from the given side lengths. If you can build a triangle, make a sketch. Side Lengths Triangle Possible? Sketch Triangle 3, 4, 5 1, 1, 3 2, 4, 7 Side Lengths Triangle Possible? Sketch Triangle 2, 3, 4 2, 3, 4 2, 3, 4 1. List some side length combinations that did make a triangle: 2. List some side length combinations that did NOT make a triangle: B. Look at your table. 1. What pattern do you see to explain why some sets of numbers make a triangle and some do not? 2. For what side length relationships can you make more than one triangle from a given set of side lengths? 3. Find three other side lengths that make a triangle. Then find three other side lengths that will NOT make a triangle. 5

6 Day 2 Homework 3.1 Introduction to two-step equations Which set(s) of side length make a triangle? a. 3, 5, 9 b. 10,20,30 c. 7,15,28 c. 19,21, 37 In your own words justify why each set that you chose makes a triangle? Which set(s) of degree measurements make a triangle? a. 30,60, 90 b. 50, 85, 45 c. 45, 75, 60 c. 20, 35, 125 In your own words justify why each set that you chose makes a triangle? Solve: 3x+9=30 Solve: 4x- 36=80 X= X= Solve: 2x+14=54 Solve: 5x-35=15 X= X= 6

7 Day 3: SD 3.2: Design Challenge II Use the directions provided to draw a triangle congruent to the one below. Do all they all work? Triangle ABC #1 #2 #3 #4 #5 Does your answer differ from your neighbor s? 6. What minimum information about a triangle allows you to draw exactly one triangle? 7. Why does have three sides make a unique triangle? 8. why does having three angles NOT make a unique triangle? 7

8 Day 3: SD 3.2 HOMEWORK. Complete and CORRECT with the KEY. 1. Multiple Choice: Which of these descriptions of a triangle ABC are directions that can be followed to draw exactly ONE shape? Explain your reasoning: 2. Construct these triangles based on the criteria (use a ruler and protractor): An equilateral triangle with sides of 1.5 inches. (Hint: A right triangle with legs of 1.5 inches and 1.75 Think about the angles in an equilateral triangle.) inches. A triangle with a 25 degree angle and legs of 2.25 inches and 3.75 inches. A triangle with a 70 degree angle with sides of 1.5 inches and 2.25 inches. 8

9 Day 4: Solving multi-step equations: 7x=119 Sequence Undo Solve the equations and check to verify if answer is correct 2x + 15 = 45 X= X= 9x 7 = 7 8x 2 = 38 X= X= 15x 90 3x = 90 2x 10 + x 30 = 185 X= X= 3n + 7+5n = 31 Challenge: 10 = 10(k 9) n = k = 9

10 Angle relationship: Complementary supplementary Equation: <AOB= Angle relationship: Complementary supplementary Equation: <AOB= 2x x Angle relationship: Complementary supplementary Equation: X= <ABC= <CBD= Angle relationship: Complementary supplementary Equation: X= <ABC= <CBD= Angle relationship: Complementary supplementary Equation: X= <ABC= <CBD= 10

11 Day 5: SD 3.4: Vertical Angles Define Vertical angles: Define alternate interior angles: Example: Example: A. Use the diagram above as you work through: 1. List all pairs of vertical angles: i. & ii. & iii. & iv. & v. & vi. & vii. & vii. & 2. List all pairs of alternate interior angles: i. & ii. & iii. & iv. & 3. List all pairs of supplementary angles: i. & ii. & iii. & iv. & v. & vi. & vii. & vii. & 4. Find all of the angle measurements: A= B= C= D= E= F= G= H= I= J= K= L= M= N= O= 11

12 B. Use the diagram at right as you work through problems 1-4: 1. Suppose angle b and angle f are 80. Find and label the rest of the angles in the diagram. When two lines intersect four angles are formed. The opposite pairs of angles are called vertical angles. For example, in the diagram angles f and g are vertical angles. 2. Name the three other pairs of vertical angles in the diagram: 3. Name the eight pairs of supplementary angles in the diagram: 4. What is true about the measures of any vertical angle pair? Explain how you know. Use what you know about complementary, supplementary, and vertical angles. Write an equation then find the value of x and the size of each angle in this figure. Equation to Solve for x: x = BAE: EAF: DAC: CAB: FAD: 12

13 Day 5: SD 3.4 HOMEWORK. Complete and CORRECT with EDpuzzle If 1= 118, find all of the missing angles. 2= 4= 6= 3= 5= 7= 8= Find the missing angles and solve for x: ACB= ACD= DCE= X= C Find each angle and solve for x: 3x+30 x 10 X= ABC= CBD= A B D 13

14 Day 6: SD 3.4: Practice with All Angle Relationships Angle Relationships: Complementary angles add up to. The complement of 30 is. 30 Supplementary angles add up to. The supplement of 30 is. Vertical angles are. The vertical angle to 30 is. Write an equation and show how to find each missing angle with a number. Identify which angle relationship you used to solve the problem. See the example: Example: Equation: Equation: Equation: = = 123 Relationship: Relationship: Relationship: Supplementary angles m 1 = 65 m 2 = 67 Equation: Equation: Equation: Relationship: Relationship: Relationship: 14

15 Ok, now it s going to get trickier You need to solve for x and then find both angles. See the example: Example: Equation: Equation: 4x x + 1 = 180 7x + 12 = 180 7x = 168 x = 24 Angles: 13 = 4x + 11 = 4(24) = 3x + 1 = 3(24) + 11 What is the angle relationship? Angles: What is the angle relationship? Does my answer seem reasonable? Yes/No Does my answer seem reasonable? Yes/No Now, find the three missing angles in this problem! You re almost done! 9. Equation: Angles: 15

16 Day 6: SD Inv. 2 HOMEWORK. Complete and CORRECT with EDpuzzle. Find all of the missing angles: 2= 3= 4 = 5= 6= 7= 8= 2) 1=52 2= 2x 3) X= 2x+45 CBA= X - 15 ABE= 16

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