Answer:
D: All angles measure 60°. Which triangle is not a unique triangle?
Explanation:
A triangle is uniquely specified if any of the following sets of information are known:
- 3 sides (SSS)
- 2 sides and the included angle (SAS)
- 2 (specific) sides and a right angle (HL or LL)
- 2 angles and any side (ASA or AAS)
- 2 angles, one of which is a right angle, and the hypotenuse (HA)
where S = side, A = angle, H = hypotenuse, L = leg
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That is, all three sides, or at least one side and one angle must be specified, along with another side or angle.
If two sides and an angle are given, the angle must either be between the two sides, or opposite the longest side. (This latter condition is not generally recognized as describing a unique triangle, because the condition relating the angle and the sides is not easily summarized in an abbreviation like SSA. For a right triangle, the abbreviation is HA.)
In the HL and LL cases, we say "specific sides" because we need to know whether the given sides are both legs, or one is the hypotenuse.
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For this question, option D gives only three angles, and no sides, so no unique triangle is specified.
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The other options give unique triangles by ...