Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 1 3) 180 Rule for Triangles Objective-To find.

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Presentation transcript:

Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 1 3) 180 Rule for Triangles Objective-To find missing angles and to solve word problems involving geometric figures. Some Strategies 1) Supplementary Angles 2) Complementary Angles 4) Vertical Angles 2:6 Word Problems Involving Geometric Figures

Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 2 Supplementary Angles- Angles whose sum is 180. a b x 30 x + 30 = x = 150 Find the value of x.

Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 3 Find the supplement of the given angle. 1) 40 2) 18 3) 153 4) 65 5) 89 6) 23 7) 131 8)

Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 4 Write a variable equation and solve. Find an angle whose supplement is 30 less than twice the angle. x2x - 30 x + (2x - 30) = 180 3x - 30 = x = 210 x = 70 70

Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 5 Complementary Angles - Angles whose sum is 90. a b x 40 x + 40 = x = 50

Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 6 Find the complement of... 1) 20 2) 47 3) 100 4) the supplement of No complement the complement of the supplement of the complement of= 60

Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 7 Write a variable equation and solve. Find an angle whose complement is 20 more than three times the angle. x 3x + 20 x + 3x + 20 = 90 4x + 20 = x = 70 4 x = 17.5

Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series Rule for Triangles - the sum of the interior angles of any triangle is always 180. a b c x x = x = 180 x = 60

Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 9 Find each angle below. y +14 y y - 10 (y + 14) + (2y - 10) + (y - 20) = 180 4y - 16 = y = 196 y = 49 y + 14 = 63 2y - 10 = 88 y - 20 =

Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 10 Vertical Angles Theorem- the opposite angles of intersecting lines must be equal.

Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 11 Vertical Angles Theorem- the opposite angles of intersecting lines must be equal.

Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 12 Vertical Angles Theorem- the opposite angles of intersecting lines must be equal. Find the missing angles a, b and c. 25 a b c 155

Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 13 Vertical Angles Theorem- the opposite angles of intersecting lines must be equal. Find the missing angles a, b and c. 25 a b c 155

Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 14 Find the missing angle x 48 x = x = 92

Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 15 Find the missing angle. 119 x x = x = 63

Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 16 Use a variable equation to solve. 1) The length of a rectangle is 5 less than 3 times its width. If the perimeter is 30 ft., find its dimensions. Let x = width 3x - 5 = length x 3x - 5 2(x) + 2(3x - 5) = 30 2x + 6x - 10 = x = 40 8 x = 5 = 5 = 10

Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 17 2) An angle is 6 degrees less than 3 times its complement. Find the angle. Let x = the complement x 3x - 6 = the angle x + (3x - 6) = 90 (3x - 6) 4x - 6 = x = 96 4 x = 24 = 24 = 3(24) - 6 = 66

Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 18 3) The largest angle in a triangle is four times the smallest. The third angle is 5 more than twice the smallest. Find each angle. Let n = the smallest angle 2n + 5 = the middle angle 4n = the largest angle n 2n + 5 4n n + (2n + 5) + 4n = 180 7n + 5 = n = n = 25 = 25 = 55 = 100

Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series 19 4) The lengths of the sides of a triangle are consecutive even integers. If the perimeter is 24 inches, find the length of each side. Let x = 1st side x + 2 = 2nd side x + 4 = 3rd side x x + 2 x + 4 x + (x + 2) + (x + 4) = 24 3x + 6 = x = 18 3 x = 6 = 6 in. = 8 in. = 10 in.