Download MathMatters 3 Chapter 4 Lesson 4-5 Problem Prove the following

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MathMatters 3
Chapter 4
Lesson 4-5
Problem
Prove the following statement.
If a figure is a triangle, then it cannot have two obtuse angles.
Solution
Begin by drawing a representative triangle, such as UABC at the right.
Step 1:
Assume that the conclusion is false. That is, assume that
a triangle can have two obtuse angles. In particular, in UABC,
assume ∠A and ∠B are obtuse angles.
Step 2:
Reason logically from the assumption, as follows. By the definition of an obtuse
angle, 90° < m∠A < 180° and 90° < m∠B < 180°. Choose an angle measure xº such
that 90° < x < 180°. If xº = 91º, then m∠A + m∠B = 91° + 91° = 182°. By the
triangle-sum theorem, m∠A + m∠B + m∠C = 180°.
Step 3:
Note that the statement m∠A + m∠B = 91° + 91° = 182° has the sum of the two
angles already greater than the sum of all three angles in a triangle. Therefore, the
assumption that a triangle can have two obtuse triangles is false. The given
statement must be true.
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