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Questions and Answers
A triangle has angles measuring $30^\circ$ and $60^\circ$. Which additional piece of information is sufficient to determine the triangle's exact size and shape?
A triangle has angles measuring $30^\circ$ and $60^\circ$. Which additional piece of information is sufficient to determine the triangle's exact size and shape?
- The area of the triangle.
- The measure of the third angle.
- The length of the longest side. (correct)
- The ratio of the shortest side to the longest side.
A right triangle has legs of length 5 and 12. What is the approximate percentage increase in the length of the hypotenuse if both legs are increased by 1?
A right triangle has legs of length 5 and 12. What is the approximate percentage increase in the length of the hypotenuse if both legs are increased by 1?
- 13%
- 8% (correct)
- 5%
- 10%
A square is inscribed in a circle of radius $r$. What is the area of the square?
A square is inscribed in a circle of radius $r$. What is the area of the square?
- $ \pi r^2$
- $r^2$
- $4r^2$
- $2r^2$ (correct)
A triangle in the coordinate plane is reflected over the y-axis and then rotated $90^\circ$ clockwise about the origin. Which single transformation would produce the same final image?
A triangle in the coordinate plane is reflected over the y-axis and then rotated $90^\circ$ clockwise about the origin. Which single transformation would produce the same final image?
A point (2, -3) is translated by the vector <1, 4> and then dilated by a factor of 2 from the origin. What are the coordinates of the final image?
A point (2, -3) is translated by the vector <1, 4> and then dilated by a factor of 2 from the origin. What are the coordinates of the final image?
Flashcards
Pythagorean Theorem
Pythagorean Theorem
a² + b² = c², relates the sides of a right triangle.
Special Right Triangles
Special Right Triangles
Side lengths are in specific ratios: 45-45-90 (1:1:√2), isoceles triangle, 30-60-90 (1:√3:2).
Trigonometric Ratios
Trigonometric Ratios
Relationships between angles and sides in right triangles: sine, cosine, tangent.
Translation
Translation
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Reflection
Reflection
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Study Notes
- Find Angle Measures of a Triangle practice problems
- Pythagorean Theorem practice problems
- Special Right Triangles practice problems
- Trigonometric ratios of Triangles (finding side length and angles) practice problems
- Symmetry practice problems
- Rigid Motions practice problems
- Translations practice problems
- Reflections practice problems
- Rotations practice problems
- Dilations practice problems
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