In triangle , an angle bisector from vertex is perpendicular to side . If and , what is the length of ?
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
Triangle has vertices , , and . Under which transformation(s) will the length remain equal to after the transformation?
A
Dilations (scalings) with a scale factor not equal to
B
Rigid motions such as translations, rotations, and reflections
C
Only translations
D
Shears
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Verified step by step guidance1
Understand that the length of a segment between two points is preserved only under transformations that do not change distances, called rigid motions.
Recall that rigid motions include translations (sliding the figure), rotations (turning the figure), and reflections (flipping the figure), all of which preserve lengths.
Recognize that dilations (scalings) with a scale factor not equal to 1 change the size of the figure, thus changing the length of segment AB.
Note that shears distort the shape by slanting it, which alters lengths and angles, so segment AB's length will not remain the same.
Conclude that only rigid motions—translations, rotations, and reflections—will keep the length AB equal to A'B' after the transformation.
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