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Main Idea and New Vocabulary
NGSSS
Key Concept: Angles of a Triangle
Example 1: Find Angle Measures
Example 2: Use Ratios to Find Angle Measures
Key Concept: Classify Triangles
Example 3: Classify Triangles
Example 4: Classify Triangles
Five-Minute Check
• Find missing angle measures in triangles.
• triangle
• scalene triangle
• acute triangle
• isosceles triangle
• right triangle
• equilateral
triangle
• obtuse triangle
MA.8.G.2.3 Demonstrate that the sum of the
angles in a triangle is 180-degrees and
apply this fact to find unknown measure of
angles, and the sum of angles in polygons.
Find Angle Measures
PARK The city park shown is
in the shape of a triangle. Find
the value of x.
x + 36 + 36 = 180
x + 72 = 180
– 72
– 72
x = 108
Write the equation.
Simplify.
Subtract.
Simplify.
Answer: The value of x is 108°.
STONES The paver stone
shown below is in the shape of a
triangle. Find the value of x.
A. 39°
B. 56°
C. 73°
D. 146°
Use Ratios to Find Angle
Measures
The measures of the angles of ΔDEF are in the
ratio 1:2:3. What are the measures of the angles?
Use Ratios to Find Angle
Measures
x + 2x + 3x = 180
6x = 180
x = 30
Write the equation.
Combine like terms.
Simplify.
Since x = 30, 2x = 2(30) or 60, and 3x = 3(30) or 90.
Answer: The measures of the angles are
30°, 60°, and 90°.
The measures of the angles of ΔQRS are in the
ratio 1:3:6. What are the measures of the angles?
A. 18°, 36°, 54°
B. 18°, 54°, 108°
C. 15°, 45°, 90°
D. 30°, 60°, 90°
Classify Triangles
Classify the triangle by its angles and by its
sides.
The triangle has a right angle and no congruent
sides.
Answer: It is a right scalene triangle.
Classify the triangle by its angles and by its
sides.
A. acute scalene
B. acute isosceles
C. obtuse scalene
D. obtuse isosceles
Classify Triangles
Classify the triangle by its angles
and by its sides.
The triangle has all acute angles and two congruent
sides.
Answer: It is an acute isosceles triangle.
Classify the triangle by its angles and by its
sides.
A. acute scalene
B. acute isosceles
C. right scalene
D. right isosceles
Find the value of x in the triangle.
A. 53°
B. 80°
C. 90°
D. 127°
Find the value of x in the triangle.
A. 15
B. 30
C. 34
D. 71
Three sides of a triangle measure 3 centimeters,
4 centimeters, and 5 centimeters. Classify the
triangle by its sides.
A. scalene
B. isosceles
C. equilateral
Two angles of a triangle measure 25° and 45°.
Classify the triangle by its angles.
A. acute
B. obtuse
C. right
All three angles of a triangle measure 60°. Can
you classify the triangle by its sides? Explain.
A. Yes; if all three angles of a triangle are
congruent, then all three sides are
congruent, and the triangle is equilateral.
B. No; you do not know the lengths of the sides.
Which of the following triangles could NOT be
classified as isosceles?
A. equilateral
B. scalene
C. acute
D. right