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

Over Lesson 10–2

A. rational

B. whole

C. irrational

D. rational, integer

Name all the sets of numbers to which 0.54 belongs?

__

Over Lesson 10–2

A. >

B. <

C. ≥

D. =

Over Lesson 10–2

Which list of numbers is correctly ordered from least to greatest?

A.

B.

C.

D.

Over Lesson 10–2

A. –6, 6

B. 6

C. –3.5, 3.5

D. 3.5

Solve y2 = 12. Round to the nearest tenth if necessary.

Over Lesson 10–2

A. 6.5 ft

B. 6.6 ft

C. 6.7 ft

D. 6.8 ft

Over Lesson 10–2

Which of the following is an example of an irrational number?

A.

B.

C.

D.

You solved equations by adding or subtracting.(Lesson 4–3)

• Find the missing angle measure of a triangle.

• Classify triangles by properties and attributes.

• line segment

• triangle

• vertex

• congruent

Find Angle Measures

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 mF = 47°.

Find the value of x in ΔDEF.

Write an equation.

A. 57

B. 123

C. 139

D. 303

Find the value of x in ΔMNO.

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?

Use Ratios to Find Angle Measures

10x = 180 Combine like terms.Divide each side by 10.

Answer: The measures of the angles are 36°, 54°, and 90°.

x = 18 Simplify.

Since x = 18, 2x = 2(18) or 36, 3x = 3(18) or 54, and 5x = 5(18) or 90.

2x + 3x + 5x = 180 Write the equation.

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?

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.

A. acute

B. right

C. obtuse

D. straight

A bird’s beak can open to about 80°. What kind of angle is this?

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.

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.

A. right scalene

B. obtuse scalene

C. obtuse isoceles

D. acute equilateral

A. Classify the triangle by its angles and by its sides.

A. right isoceles

B. obtuse isoceles

C. obtuse scalene

D. acute equilateral

B. Classify the triangle by its angles and by its sides.