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5-Minute Check on Lesson 4-1

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.

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5-Minute Check on Lesson 4-1

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  1. 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

  2. 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

  3. 4.2 Angles of Triangles

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

  5. X Y Z Theorem 4.1 – Angle Sum Theorem The sum of the measures of the angles of a triangle is 180°. mX + mY + mZ = 180°

  6. Find first because the measure of two angles of the triangle are known. Example 1: Find the missing angle measures. Angle Sum Theorem Simplify. Subtract 117 from each side.

  7. Answer: Example 1: Angle Sum Theorem Simplify. Subtract 142 from each side.

  8. EXAMPLE 2: Find the missing angle measures. Answer:

  9. Theorem 4.2 – Third Angle Theorem If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangle are congruent. Abbreviation: If 2 s of one Δ are  to 2 s of another Δ, then third s are .

  10. 2 1 3 4 Exterior Angles and Triangles • An exterior angle is formed by one side of a triangle and the extension of another side (i.e. 1 ). • The interior angles of the triangle not adjacent to a given exterior angle are called the remote interior angles (i.e. 2 and 3).

  11. 2 1 3 4 Theorem 4.3 – 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. m 1 = m2 + m 3

  12. Example 3: 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.

  13. Example 3 CONT: Exterior Angle Theorem Substitution Subtract 64 from each side. If 2 s form a linear pair, they are supplementary. Substitution Simplify. Subtract 78 from each side.

  14. Answer: Example 3 CONT: Angle Sum Theorem Substitution Simplify. Subtract 143 from each side.

  15. EXAMPLE 4: Find the measure of each numbered angle in the figure. Answer:

  16. Corollaries • A corollary is a statement that can be easily proven using a theorem. • Corollary 4.1 – The acute s of a right ∆ are complementary. • Corollary 4.2 – There can be at most one right or obtuse  in a∆.

  17. GARDENING The flower bed shown is in the shape of a right triangle. Find if is 20. Example 5: Corollary 4.1 Substitution Subtract 20 from each side. Answer:

  18. The piece of quilt fabric is in the shape of a right triangle. Find if is 62. EXAMPLE 6: Answer:

  19. Assignment • Geometry: Pg. 189 #11- 35

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