Download Use Logical Reasoning

Five-Minute Check (over Lesson 10–4)
Main Idea
Example 1: Use Logical Reasoning
• Solve problems by using logical reasoning.
Use Logical Reasoning
Draw an equilateral triangle. How can you confirm
that it is equilateral? Use logical reasoning.
Understand
You know that equilateral triangles
have three congruent sides. You need
to confirm whether or not a drawn
triangle is equilateral.
Plan
Draw an equilateral triangle. Measure
the sides to confirm that all three sides
are congruent.
Use Logical Reasoning
Solve
Draw the triangle.
Measure the sides using a ruler or centimeter ruler. The
side lengths are 2.6 centimeters, 2.6 centimeters, and
2.6 centimeters. Since all three are congruent, the
triangle is equilateral.
Use Logical Reasoning
Check
Since all three sides are congruent, the
triangle is equilateral.
Do the angles in an equilateral triangle have a special
relationship?
A. Yes, there is one
obtuse angle and two
acute angles.
B. Yes, there three acute
angles, two of which
are congruent.
C. Yes, all three angles are
congruent.
D. No
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B
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End of the Lesson
Five-Minute Check (over Lesson 10–4)
Image Bank
Math Tools
Tessellations
Translations
(over Lesson 10-4)
Find the missing measure in the
triangle. Then classify the triangle
as acute, right, or obtuse.
A. 127°; acute
B. 100°; obtuse
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2.
3.
C. 90°; right
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(over Lesson 10-4)
Find the missing measure
in the triangle. Then
classify the triangle as
acute, right, or obtuse.
A. 15°; acute
B. 15°; obtuse
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2.
3.
C. 25°; right
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(over Lesson 10-4)
Three sides of a triangle measure 3 centimeters,
4 centimeters, and 5 centimeters. Classify the
triangle by its sides.
A. acute
B. equilateral
C. obtuse
D. scalene
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B
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(over Lesson 10-4)
Two angles of a triangle measure 25° and 45°.
Classify the triangle by its angles.
A. acute
B. equilateral
C. obtuse
D. scalene
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B
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(over Lesson 10-4)
All three angles of a triangle measure 60°. Can you
classify the triangle by its sides? Explain.
C.
Yes; if all three angles of a triangle are
congruent, then all three sides are congruent,
and the triangle is a right triangle.
D.
Yes; if all three angles of a triangle are
congruent, then all three sides are congruent,
and the triangle is equilateral.
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2.
3.
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No; if all three angles of a triangle are 60°,
then all three sides are not congruent, and
the triangle cannot be classified.
C
B.
B
No; it is not possible to classify the triangle by
its side as the measurements of the sides are
not given.
A
A.
(over Lesson 10-4)
Which of the following triangles could not be
classified as isosceles?
A. equilateral
B. scalene
C. acute
D. right
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B
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