Chapter 13 (PDF)
Chapter 13 (PDF)
Chapter 13 (PDF)
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Lesson <strong>13</strong>.5 • Indirect Proof<br />
Name Period Date<br />
1. Complete the indirect proof of the conjecture: In a triangle the side<br />
opposite the larger of two angles has a greater measure.<br />
Given: ABC with mA mB<br />
Show: BC AC<br />
Proof: Assume ________________<br />
Case 1: BC AC<br />
If BC AC, then ABC is ________________ by _______________.<br />
By _______________, A B, which contradicts ______________.<br />
So, BC AC.<br />
Case 2: BC AC<br />
If BC AC, then it is possible to construct point D on CA such that<br />
CD CB, by the Segment Duplication Postulate. Construct DB, by<br />
the Line Postulate. DBC is ________________. Complete the proof.<br />
A<br />
D 4<br />
1<br />
C<br />
2<br />
3<br />
B<br />
In Exercises 2–5, write an indirect proof of each conjecture.<br />
2. Given: AD AB, DC BC<br />
A<br />
Show: DAC BAC<br />
3. If two sides of a triangle are not congruent, then the angles<br />
opposite them are not congruent.<br />
4. If two lines are parallel and a third line in the same plane intersects<br />
one of them, then it also intersects the other.<br />
B<br />
88 CHAPTER <strong>13</strong> Discovering Geometry Practice Your Skills<br />
A<br />
C<br />
C<br />
D<br />
B<br />
©2008 Kendall Hunt Publishing
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