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Example 4-4b Objective Identify and classify triangles

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Example 4-4b Vocabulary Triangle A polygon that has three sides and three angles

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Example 4-4b Vocabulary Acute triangle A triangle having three acute angles

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Example 4-4b Vocabulary Right triangle A triangle having one right angle

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Example 4-4b Vocabulary Obtuse triangle A triangle having one obtuse angle

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Example 4-4b Vocabulary Congruent segments Sides of a triangle having the same length

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Example 4-4b Vocabulary Scalene triangle A triangle having no congruent sides

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Example 4-4b Vocabulary Isosceles triangle A triangle having at least two congruent sides

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Example 4-4b Vocabulary Equilateral triangle A triangle having three congruent sides

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Lesson 4 Contents Example 1Find Angle Measures of Triangles Example 2Find a Missing Measure Example 3Classify Triangles Example 4Classify Triangles

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Example 4-1a PLANES An airplane has wings that are shaped like triangles. Find the missing measure. 1/4 The sum of the measures is 180 0 Add angles together x0x0 + 112 0 + 47 0 Remember: sum = 180 0 = 180 0

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Example 4-1a PLANES An airplane has wings that are shaped like triangles. Find the missing measure. 1/4 Bring down x 0 x0x0 + 112 0 + 47 0 = 180 0 x0x0 Combine “like” terms + 159 0 Bring down = 180 0 = 180 0 Ask “what is being done to the variable?” The variable is being added by 159 0 Do the inverse on both sides of the equal sign

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Example 4-1a PLANES An airplane has wings that are shaped like triangles. Find the missing measure. 1/4 x0x0 + 112 0 + 47 0 = 180 0 x0x0 + 159 0 = 180 0 Bring down x 0 + 159 0 x 0 + 159 0 Subtract 159 0 - 159 0 Bring down = 180 0 = 180 0 Subtract 159 0 - 159 0 Bring down x 0 x0x0 Combine “like” terms + 0 0 Bring down = =

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Example 4-1a PLANES An airplane has wings that are shaped like triangles. Find the missing measure. 1/4 x0x0 + 112 0 + 47 0 = 180 0 x0x0 + 159 0 = 180 0 x 0 + 159 0 - 159 0 = 180 0 - 159 0 x0x0 Combine “like” terms + 0 0 = 21 0 Use the Identify Property to add x 0 + 0 0 x = 21 0 Answer:

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Example 4-1b SEWING A piece of fabric is shaped like a triangle. Find the missing measure. Answer: x = 49 1/4 x

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Example 4-2a ALGEBRA Find m A in ABC if m A m B and m C 80 . Draw the triangle 2/4 Define m A as x m A m B x

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Example 4-2a ALGEBRA Find m A in ABC if m A m B and m C 80 . 2/4 Since m A is x and m m B then B can also be x x x + x = 2x 2 The sum of the measures is 180 0

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Example 4-2a ALGEBRA Find m A in ABC if m A m B and m C 80 . 2/4 Add 80 0 for the m C x Put the = 180 0 since this is the sum 2 Solve for the unknown + 80 0 = 180 0

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Example 4-2a ALGEBRA Find m A in ABC if m A m B and m C 80 . 2/4 x 2 + 80 0 = 180 0 Ask “what is being done to the variable term (2x)?” The variable term is being added by 80 0 Do the inverse on both sides of the equal sign Bring down 2x + 80 0 2x + 80 0 Subtract 80 0 - 80 0 Bring down = 180 0 = 180 0 Subtract 80 0 - 80 0

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Example 4-2a ALGEBRA Find m A in ABC if m A m B and m C 80 . 2/4 x 2 + 80 0 = 180 0 2x + 80 0 - 80 0 = 180 0 - 80 0 Bring down 2x Combine “like” terms 2x + 0 0 Bring down = = Combine “like” terms 100 0 Use the Identify Property to add 2x + 0 0 2x = 100 0 Ask “what is being done to the variable?” The variable is being multiplied by 2

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Example 4-2a ALGEBRA Find m A in ABC if m A m B and m C 80 . 2/4 x 2 + 80 0 = 180 0 2x + 80 0 - 80 0 = 180 0 - 80 0 2x + 0 0 =100 0 2x = 100 0 Do the inverse on both sides of the equal sign Bring down 2x = 100 0 2x = 100 0 Using the fraction bar, divide both sides by 2 2 2 Combine “like” terms 1 x = 50 0 Use the Identify Property to multiply 1 x x = 50 0 Since you defined m A as x and x = 50 0 then m A = 50 0 m A = 50 0 Answer:

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Example 4-2b ALGEBRA Find m J in JKL if m J m K and m L 100 . Draw the triangle then solve Answer: m J = 40 2/4

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Example 4-3a Classify the triangle by its angles and its sides. Obtuse All triangles have 3 names First, middle and last (just like you) First: classify angle 3/4 One angle greater than 90 0 meets the definition of obtuse angle

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Example 4-3a Classify the triangle by its angles and its sides. Obtuse Next, classify by sides 3/4 2 sides congruent meets the definition of isosceles Isosceles All triangles have the last name as “triangle” Triangle Answer:

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Example 4-3b Classify the triangle by its angles and its sides. Answer: Right Scalene Triangle 3/4

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Example 4-4a Classify the triangle by its angles and its sides. 4/4 All triangles have 3 names First, middle and last (just like you) First: classify angle All angles are less than 90 0 meets the definition of acute angle Acute

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Example 4-4a Classify the triangle by its angles and its sides. 4/4 Acute Next, classify by sides No sides have a congruent symbol so meets the definition of scalene Scalene All triangles have the last name as “triangle” Triangle Answer:

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Example 4-4b Classify the triangle by its angles and its sides. Answer: Acute Equilateral Triangle * 4/4

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End of Lesson 4 Assignment Lesson 10:4Triangles3 - 24 All

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