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Lesson 4-2

Lesson 4-2. Angles of Triangles. Transparency 4-2. 5-Minute Check on Lesson 4-1. Refer to the figure. 1. Classify  RST as acute, equiangular, obtuse, or right. 2. Find y if  RST is an isosceles triangle with RS  RT . Refer to the figure.

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Lesson 4-2

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  1. Lesson 4-2 Angles of Triangles

  2. Transparency 4-2 5-Minute Check on Lesson 4-1 Refer to the figure. 1. Classify RST as acute, equiangular, obtuse, or right. 2. Find y if RST is an isosceles triangle with RSRT. Refer to the figure. 3. Find x if ABC is an equilateral triangle. 4. Name the right triangles if ADCB. 5. Classify MNO as scalene, isosceles, or equilateral if MN = 12, NO = 9, and MO = 15. 6. Choose the angle measures that represent the angles of an obtuse triangle. Standardized Test Practice: D C 30, 50, 100 50, 70, 60 A B 45, 45, 90 60, 60, 60

  3. Transparency 4-2 5-Minute Check on Lesson 4-1 Refer to the figure. 1. Classify RST as acute, equiangular, obtuse, or right. obtuse 2. Find y if RST is an isosceles triangle with RSRT. 12 Refer to the figure. 3. Find x if ABC is an equilateral triangle. 4 4. Name the right triangles if ADCB. ACD andABD 5. Classify MNO as scalene, isosceles, or equilateral if MN = 12, NO = 9, and MO = 15. scalene 6. Choose the angle measures that represent the angles of an obtuse triangle. Standardized Test Practice: D C 30, 50, 100 50, 70, 60 A B 45, 45, 90 60, 60, 60

  4. Objectives • Apply the Angle Sum Theorem • Apply the Exterior Angle Theorem

  5. Vocabulary • Exterior Angle – is formed by one side of a triangle and the extension of another side • Remote Interior Angle – interior angles not adjacent to the given exterior angle • Corollary – a statement that can be easily proven using a particular theorem

  6. Theorems & Corollaries • Angle Sum Theorem – The sum of the measures of the angles of a triangle is 180°. • Third Angle Theorem – If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent. • Exterior Angle Theorem – The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. • Corollaries: • the acute angles of a right triangle are complementary • there can be at most one right or obtuse angle in a triangle

  7. A Triangle’s Angles mA + mB + mC = 180° B Remote Interior Angles to A Exterior Angle to A C A mExtA = mB + mC – Exterior  Theorem mExtA + mA = 180° – Linear Pair

  8. Answer: Find the missing angle measures. Find m1 first because the measure of two angles of the triangle are known. Angle Sum Theorem Simplify. Subtract 117 from each side. Angle Sum Theorem Simplify. Subtract 142 from each side.

  9. Find the missing angle measures. Answer:

  10. Find the measure of each numbered angle in the figure. Exterior Angle Theorem Simplify. If 2 s form a linear pair, they are supplementary. Substitution Subtract 70 from each side. Exterior Angle Theorem Substitution Subtract 64 from each side.

  11. Answer: If 2 s form a linear pair, they are supplementary. Substitution Simplify. Subtract 78 from each side. Angle Sum Theorem Substitution Simplify. Subtract 143 from each side.

  12. Find the measure of each numbered angle in the figure. Answer:

  13. GARDENING The flower bed shown is in the shape of a right triangle. Find if is 20. Corollary 4.1 Substitution Subtract 20 from each side. Answer:

  14. The piece of quilt fabric is in the shape of a right triangle. Find if is 32. Answer:

  15. Summary & Homework • Summary: • The sum of the measures of the angles of a triangle is 180 • The measure of an exterior angle is equal to the sum of the measures of the two remote interior angles • Homework: • pg 188-9: 5-9, 18-23

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