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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 Lesson Menu

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

A. > B. < C. ≥ D. = 5-Minute Check 2

Which list of numbers is correctly ordered from least to greatest? 5-Minute Check 3

Solve y2 = 12. Round to the nearest tenth if necessary. B. 6 C. –3.5, 3.5 D. 3.5 5-Minute Check 4

A. 6.5 ft B. 6.6 ft C. 6.7 ft D. 6.8 ft 5-Minute Check 5

Which of the following is an example of an irrational number? D. 5-Minute Check 6

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

line segment triangle vertex congruent Vocabulary

Concept A

Find the value of x in ΔDEF. Find Angle Measures Find the value of x in ΔDEF. Write an equation. 100 + 33 + x = 180 Substitution 133 + x = 180 Simplify. 133 – 133 + x = 180 – 133 Subtract 133 from each side. x = 47 Simplify. Answer: x is 47, so mF = 47°. Example 1

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

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? Example 2

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

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

Concept B

Answer: 45° is less than 90°, so it is an acute angle. 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. Example 3

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

Concept C

Concept D

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

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

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

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

End of the Lesson