Given triangle , which equation could be used to find using the Law of Sines?
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 where , , and , which triangles in the diagram are congruent?
A
No triangles in the diagram are congruent
B
and are congruent
C
and are similar but not congruent
D
and are congruent
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Verified step by step guidance1
Identify the given information: angles \( \angle A = \angle D \) and \( \angle B = \angle E \), and the ratio of sides \( \frac{AB}{DE} = \frac{BC}{EF} \).
Recall that two triangles are congruent if all corresponding sides and angles are equal, or if they satisfy congruence criteria such as SAS, ASA, or SSS.
Note that the given information includes two pairs of equal angles and a proportionality (ratio) between two pairs of sides, not equality of sides.
Recognize that having two equal angles and proportional sides corresponds to the criteria for similarity (AA or SAS similarity), not congruence, because side lengths are proportional, not necessarily equal.
Conclude that triangles \( ABC \) and \( DEF \) are similar but not necessarily congruent based on the given angle equalities and side ratios.
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