Download Answers Teacher Copy p. 281 Lesson 22

Answers
Teacher Copy
Lesson 22-2
Properties of Triangles and Angle Measures
Learning Targets
Classify angles by their measures.
Classify triangles by their angles.
Recognize the relationship between the lengths of sides and measures of angles in a
triangle.
Recognize the sum of angles in a triangle.
Interactive Word Wall (Learning Strategy)
Definition
Visually displaying vocabulary words to serve as a classroom reference of words and groups of
words as they are introduced, used, and mastered over the course of a year
Purpose
Provides a visual reference for new concepts, aids understanding for reading and writing, and
builds word knowledge and awareness
Summarizing (Learning Strategy)
Definition
Giving a brief statement of the main points in a text
Purpose
Assists with comprehension and provides practice with identifying and restating key information
Visualization (Learning Strategy)
Definition
Picturing (mentally and/or literally) what is read in the text
Purpose
Increases reading comprehension and promotes active engagement with the text
Graphic Organizer (Learning Strategy)
p. 281
Definition
Arranging information into maps and charts
Purpose
Builds comprehension and facilitates discussion by representing information in visual form
Suggested Learning Strategies
Interactive Word Wall, Summarizing, Visualization, Graphic Organizer
p. 285p. 284p. 283p. 282
Math Tip
If the rays are too short to measure with a protractor, extend the length of the sides of the
angle.
Math Tip
A box at the vertex of an angle indicates an angle with measure 90°.
Another way to classify triangles is by their angles. A right angle has a measure of 90°. An acute
angle has a measure of less than 90°. An obtuse angle is greater than 90° and less than 180°.
1. Use the angles shown.
a. Estimate the measure of each angle.
∠A ≈
∠B ≈
∠C ≈
∠D ≈
∠E ≈
∠F ≈
b. Use appropriate tools strategically. Use a protractor to find the measure of each angle
to the nearest degree. Then classify each angle as acute, obtuse, or right by its
measure.
∠A =
∠B =
∠C =
∠D =
∠E =
∠F =
Now Mr. Mira draws the following examples of triangles.
Acute Triangles
Obtuse Triangles
Right Triangles
2. Based on Mr. Mira's examples, describe each type of triangle.
a. acute triangle
b. obtuse triangle
c. right triangle
3. A triangle can be labeled using both its angle measures and the lengths of its sides.
a. Label the triangles that Mr. Mira drew by side length.
b. Choose one of the triangles and give the two labels that describe it.
c. Explain how the two labels together provide a better description of the triangle than
either one alone. Share your ideas with our group and be sure to explain your
thoughts using precise language and specific details to help group members
understand your ideas and reasoning.
Mr. Mira has his class investigate the sum of the measures of a triangle. Students measured the
angles of some scalene, isosceles, and equilateral triangles. They recorded their results as shown.
Scalene Triangles
Isosceles Triangles
Equilateral Triangles
4.
a. Find the sum of the angle measures for each triangle.
The Triangle Sum Theorem states that the sum of the three angle measures in any triangle is
always equal to a certain number.
Math Terms
A theorem is a statement or conjecture that has been proven to be true.
Technology Tip
You can use geometry software to construct triangles with specific interior angle measures.
Use the protractor tool to measure the angles of a triangle.
b. What is the sum of the angle measures in any triangle?
The Triangle Sum Theorem allows you to find the measure of the third angle in a triangle when
you are given the other two angle measures.
5. Students played a game in which they chose two angle measures of a triangle and then
determined the third angle measure. What must be true about the two angle measures the
students choose?
6. Some of the angle measures students created for triangles are shown. For each pair of
angle measures, find the measure of the third angle in the triangle.
a. 43°, 94°
b. 38°, 52°
c. 57°, 39°
d. 140°, 12°
e. 60°, 60°
The angle measures of a triangle can be used to determine if the triangle is scalene, isosceles, or
equilateral. Look back at the triangles Mr. Mira drew.
Scalene Triangles
Isosceles Triangles
Equilateral Triangles
Math Terms
A triangle with three equal angles is called equiangular.
7. Compare the angle measures of the triangles. Look for patterns in Mr. Mira's examples to
help you determine if the triangles described below are scalene, isosceles, or equilateral.
a. a triangle with three different angle measures
b. a triangle with exactly two congruent angle measures
c. an equiangular triangle
8. Look back at Item 6. Classify each triangle by its side lengths and by its angle measures.
Another relationship exists between the angles and the sides of a triangle. In a triangle, the side
opposite the angle with the greatest measure is the longest side.
9. Compare the angle measure to the side opposite the angle in a scalene triangle. What is
true about the side opposite the angle with the least measure?
Check Your Understanding
For Items 10–12, sketch a triangle described by each pair of words below or state that it is
not possible. Use tick marks and right angle symbols where appropriate. If it is not possible
to sketch a triangle, explain why not.
10. scalene, obtuse
11. isosceles, acute
12. equilateral, right
13. Two angles in a triangle measure 35° and 50°. Explain how to find the measure of the third
angle.
Lesson 22-2 Practice
For Items 14–19, sketch a triangle described by each pair of words below or state that it is
not possible. If it is not possible to sketch a triangle, explain why not.
14. scalene, right
p. 286
15. isosceles, obtuse
16. equilateral, acute
17. isosceles, right
18. scalene, acute
19. equilateral, obtuse
20. Use appropriate tools strategically. Use a ruler and a protractor to sketch a triangle that is
scalene and has an angle that measures 30°. Is the triangle acute, right, or obtuse?
Explain.
21. Two angles in a triangle measure 65° each. What is the measure of the third angle?
22. Reason quantitatively and abstractly. Find the missing angle measure or measures in
each triangle below. Then classify the triangle by both its angle measures and its side
lengths.
a. The three angles in a triangle have the same measure.
b. Two angles in a triangle measure 45° each.
c. Two angles in a triangle measure 25° and 50°.
23. Construct viable arguments. Determine whether each statement below is always true,
sometimes true, or never true. Explain your reasoning.
a. The acute angles of an isosceles triangle add up to 90°.
b. An isosceles triangle has two equal angles.
c. An equilateral triangle has a right angle.
d. The largest angle of a scalene triangle can be opposite the shortest side.
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