Four students each select three pieces labeled with side lengths and angle measures: Don chooses , , ; Margo chooses , , ; Sonji chooses , , ; Liam chooses , , . According to the Law of Sines, which student chose pieces that can be used to construct a triangle?
Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles40m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
- OLD 1. Angles and the Trigonometric Functions Coming soon
- OLD 2. Trigonometric Functions graphs, Inverse Trigonometric Functions Coming soon
- OLD 3. Trigonometric Identities and Equations Coming soon
- OLD 4. Laws of Sines, Cosines and Vectors Coming soon
- OLD 5. Complex Numbers, Polar Coordinates and Parametric Equations Coming soon
- NEW (not used) 7. Laws of Sines, Cosines and Vectors Coming soon
- NEW (not used) 8. Vectors Coming soon
- NEW(not used) 9. Polar equations Coming soon
- NEW (not used) 11. Graphing Complex Numbers Coming soon
7. Non-Right Triangles
Law of Sines
Multiple Choice
Given two triangles, and , can they be proven congruent by the Side-Side-Side (SSS) criterion? Choose the best explanation.
A
Yes, because the Law of Sines guarantees congruence if two angles and a side are known.
B
Yes, because any two triangles sharing two vertices are always congruent by SSS.
C
No, because SSS requires all three corresponding sides to be equal, and without information about side and , congruence cannot be established.
D
No, because SSS can only be used for right triangles.
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Verified step by step guidance1
Identify the triangles involved: \( \triangle abc \) and \( \triangle adc \). Notice that they share vertices \( a \) and \( c \), but the other vertices differ (\( b \) and \( d \)).
Recall the Side-Side-Side (SSS) congruence criterion: two triangles are congruent by SSS if all three pairs of corresponding sides are equal in length.
Check which sides are known or shared: the sides \( ab \) and \( ac \) in the first triangle correspond to \( ad \) and \( ac \) in the second triangle. However, the side \( bc \) in the first triangle corresponds to \( dc \) in the second triangle, and there is no information given about these two sides.
Since the lengths of sides \( bc \) and \( dc \) are unknown or not stated to be equal, the SSS criterion cannot be applied to prove congruence between these two triangles.
Therefore, without all three pairs of corresponding sides known to be equal, the triangles cannot be proven congruent by the SSS criterion.
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