1.5 geo concepts perimeter, segments, and angles 2017 ink.notebook. August 31, Page 34. Page 33 Page Two-Step Geometry Concepts

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1 1.5 geo concepts perimeter, segments, and angles 2017 ink.notebook Page 34 Page 33 Page Two-Step Geometry Concepts Lesson Objectives Standards 1.4 Using Algebra for Geometry Concepts Rules Page 35 Press the tabs to view details. 1

2 Standards Lesson Notes N.Q.3 I will use limitations on geometry concepts to understand that angles and lengths cannot be negative A.CED.1 I will create an equation from the properties of complementary angles and use it to solve for the missing angles A.CED.1 I will create an equation from the properties of supplementary angles and use it to solve for the missing angles A.CED.1 I will create an equation from the properties of triangle sum and use it to solve for the missing angles. A.CED.1 I will create an equation from the properties of segment length and use it to solve for the missing segments. A.CED.1 I will create an equation from the properties of perimeter and use it to solve for the missing segments. A.CED.3 I will understand that when solving equations derived from geometric concepts that the answer cannot have a negative angle or length A.REI.1 I will explain each step in solving a two step equation A.REI.3 I will solve a linear 2 step equation Lesson Objectives Press the tabs to view details. Standards Lesson Notes A.CED.1 Create equations and inequalities in one variable and use them to solve problems. A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. A.REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Segment Length The pieces of a segment ADD up to the whole segment x 5 A B C AC = 8 m Midpoint The EXACT middle of a segment Examples: x + 5 = AB = BC A B C B is the midpoint of AC Will usually be told what entire segment equals Has No angles because it has No arrows Will be told it is the midpoint. Sides are equal to each other, not a measurement. 2x 20 A B C 2x = 20 Complementary 2 angles that add up to = 90 Supplementary 2 angles that add up to = 180 Will have a box in the corner to show it is 90 5x x + 24 = 90 Linear pair 2 angles that make a "line" or a straight angle 4x x + 36 = 180 2

3 Triangle Sum The sum of the measures of the interior angles of a triangle equal 180 must be the angles INSIDE the triangle 1) x 10 cm _ = 180 2x 3x 50 5x + 50 = 180 Perimeter = 32 cm 2) M 3x - 8 2x + 4 N J 6x - 15 Perimeter = 25 ft MN = NJ = MJ = 3

4 1.5 geo concepts perimeter, segments, and angles 2017 ink.notebook 3) 2n R 4) 4n - 5 S R = 19 cm 6x ft B C A B is the midpoint of AC Equation Equation n = RS = AB = S = AC = 5) 6) D 2p - 9 F W 2x + 6 Z 4x 30 E G Y p = mûdef = mûwyz = mûdeg = mûzy = 4

5 1.5 geo concepts perimeter, segments, and angles 2017 ink.notebook 7) 8) S 3x x + 45 R Q P W 3x + 4 2x + 6 U mûpqs = mûuw = mûsqr = mûwx = A X 9) Equation 6x + 4 C 3x + 1 5x B mûb = mûa = mûc = 5

6 a) 7 m 2x On Your Whiteboards Perimeter = 25 m _ 10 m Pull Pull Pull b) 3x x M N O MO = 20 in On the Worksheet MN = NO = 6

7 1. Perimeter = 84 in R 3x - 6 2x T x S Homework RS = RT = ST = 2. 4x - 3 T 2x + 5 U 3. 2x U x + 10 Perimeter = 68 m 7x - 12 Perimeter = 62 in Z W TU = U = U = X = T = 7

8 in 6x + 1 6x x N B Q A P x - 12 x 4x in M Y Z W Z Y NQ = 56 km P is the midpoint of A Y is the midpoint of MZ WY = 150 cm NB = P = MY = WZ = BQ = A = MZ = 8) R 7n n S T P 9) W 2x - 5 Z x + 14 Y 10) S 11) W 8x 4x x x + 5 P Q R U X n = m RST = m TSP = m WYZ = m ZY = m PQS = m SQR = m UW = m WX = 8

9 12) M 11x ) T 5x + 39 Answers: 1) x = 15, 39 in, 30 in, 15 in 3) x = 7, 17 in, 14 in 5) x = 12, 73 in, 146 in 7) x = 18, 132 cm 9) x = 27, 49, 41 11) x = 27, 121, 59 13) x = 9, 77, 19 A 5x - 3 2x - 1 P S 3x x - 8 R Equation Equation m M = m P = m S = m R = 1 True False Perimeter measures the distance around a figure or area. True or False Extra Practice 9

10 2 What is the formula for finding the perimeter of a rectangle? Multiple choice 3 The width of a rectangle is 3 cm less than its length. The perimeter is 18 cm. What is the length? Numeric A P = l + w B P = 2(l + w) C D P = (l + w)/2 P = l x w 4 The length of a rectangle is 4 in. more than the width. The perimeter is 20 in. What is the width? Numeric 5 The length of a rectangle is triple the width. The perimeter is 48. What are the dimensions? Sorting 1 4 by by by by 15 10

11 Word problems Word problems Two angles are complementary. The larger angle is 5 times greater than the smaller angle. Find the measure of the 2 angles. Two angles are supplementary. The larger angle is 8 times greater than the smaller angle. Find the measure of the 2 angles. Two angles are complementary. The measure of the angles are in a ratio of 7:5. Find the measure of the angles. The measure of the supplement of an angle is 10 o more than four times the original angle. Find the measure of the two angles. 9) D F 2p +8 E 3p +2 G p = m DEF = m DEG = 11