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Lesson Menu Five-Minute Check (over Lesson 10–2) Then/Now New Vocabulary Key Concept: Angles of a Triangle Example 1: Find Angle Measures Example 2: Use Ratios to Find Angle Measures Key Concept: Types of Angles Example 3: Real-World Example: Classify Angles Key Concept: Classify Triangles by Angles Key Concept: Classify Triangles by Sides Example 4: Classify Triangles

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Over Lesson 10–2 5-Minute Check 1 A.rational B.whole C.irrational D.rational, integer Name all the sets of numbers to which 0.54 belongs? __

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Over Lesson 10–2 5-Minute Check 2 A.> B.< C. D.=

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Over Lesson 10–2 5-Minute Check 3 Which list of numbers is correctly ordered from least to greatest? A. B. C. D.

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Over Lesson 10–2 5-Minute Check 4 A.–6, 6 B.6 C.–3.5, 3.5 D.3.5 Solve y 2 = 12. Round to the nearest tenth if necessary.

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Over Lesson 10–2 5-Minute Check 5 A.6.5 ft B.6.6 ft C.6.7 ft D.6.8 ft

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Over Lesson 10–2 5-Minute Check 6 Which of the following is an example of an irrational number? A. B. C. D.

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Then/Now You solved equations by adding or subtracting. (Lesson 4–3) Find the missing angle measure of a triangle. Classify triangles by properties and attributes.

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Vocabulary line segment triangle vertex congruent

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Concept A

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Example 1 Find Angle Measures x =180Substitution x=180Simplify. 133 – x=180 – 133 Subtract 133 from each side. x=47Simplify. Answer: x is 47, so m F = 47°. Find the value of x in ΔDEF. Write an equation.

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Example 1 A.57 B.123 C.139 D.303 Find the value of x in ΔMNO.

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Example 2 Use Ratios to Find Angle Measures ALGEBRA The measures of the angles of a triangle are in the ratio 2:3:5. What are the measures of the angles?

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Example 2 Use Ratios to Find Angle Measures 10x =180Combine like terms. Divide each side by 10. Answer: The measures of the angles are 36°, 54°, and 90°. x =18Simplify. Since x = 18, 2x = 2(18) or 36, 3x = 3(18) or 54, and 5x = 5(18) or 90. 2x + 3x + 5x = 180Write the equation.

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Example 2 A.12°, 60°, 84° B.30°, 50°, 70° C.36°, 60°, 84° D.40°, 60°, 80° ALGEBRA The measures of the angles of a certain triangle are in the ratio 3:5:7. What are the measures of the angles?

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Concept B

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Example 3 Classify Angles HUMAN JAWS Humans have jaws that can open to about 45°. What type of angle is formed by the jaws of a human? Answer: 45° is less than 90°, so it is an acute angle.

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Example 3 A.acute B.right C.obtuse D.straight A birds beak can open to about 80°. What kind of angle is this?

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Concept C

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Concept D

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Example 4 Classify Triangles A. Classify the triangle below by its angles and by its sides. Answer: The triangle is an obtuse scalene triangle. Angles: The triangle has an obtuse angle. Sides: The triangle has no congruent sides.

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Example 4 Classify Triangles B. Classify the triangle by its angles and by its sides. Answer: The triangle is a right isosceles triangle. Angles: The triangle has a right angle. Sides: The triangle has two congruent sides.

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Example 4 CYP A A.right scalene B.obtuse scalene C.obtuse isoceles D.acute equilateral A. Classify the triangle by its angles and by its sides.

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Example 4 CYP B A.right isoceles B.obtuse isoceles C.obtuse scalene D.acute equilateral B. Classify the triangle by its angles and by its sides.

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End of the Lesson

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