The Pythagorean Theorem
A right triangle has legs of lengths 6 cm and 8 cm. What is the length of the hypotenuse?
10cm
A triangle has vertices at A(1, 2), B(3, 5), and C(4, 1). If the triangle is translated 3 units left and 2 units up, what are the coordinates of the new vertex A'?
A'(-2, 4)
A cylinder has a radius of 3 cm and a height of 7 cm. What is its volume in terms of pi?
63 pi cm^3
Two parallel lines are cut by a transversal. If one interior angle measures 115 degrees, what is the measure of its consecutive (same-side) interior angle?
65 degrees
Rectangle A is congruent to Rectangle B. If Rectangle A has a perimeter of 24 cm, what is the perimeter of Rectangle B?
24cm
The hypotenuse of a right triangle is 13 inches and one leg is 5 inches. What is the length of the other leg?
12 inches
The point P(-4, 7) is reflected across the x-axis. What are the coordinates of its image, P'?
P'(-4, -7)
A cone has a radius of 6 inches and a height of 10 inches. What is its volume to the nearest tenth?
377.0 inches^3
In a right triangle, one acute angle measures 38 degrees. What is the measure of the other acute angle?
52 degrees
Triangle ABC is similar to Triangle DEF. If the sides of ABC are 3, 4, and 5, and the shortest side of DEF is 9, what is the scale factor from ABC to DEF?
3
A 10 foot ladder leans against a wall. The base of the ladder is 6 feet away from the wall. How high up the wall does the ladder reach?
8 feet
A square is rotated 90 degrees clockwise about the origin. If one vertex was at (2, -3), what are its new coordinates?
(-3, -2)
What is the volume of a sphere with a radius of 3 meters in terms of pi?
36 pi meters^3
An exterior angle of a triangle measures 120 degrees. If one of its remote interior angles measures 50 degrees, what is the measure of the other remote interior angle?
70 degrees
If two shapes are similar, their corresponding sides are proportional. What is true about their corresponding angles?
They are equal
What is the distance between the points (1, 2) and (4, 6) on a coordinate plane?
5 units
Triangle XYZ is dilated by a scale factor of k = 3 with the origin as the center of dilation. If vertex X is at (2, 4), what are the coordinates of X'?
X'(6, 12)
A cylindrical soda can holds a volume of 36 pi cubic inches. If its radius is 2 inches, what is its height?
9 inches
If two lines intersect and create vertical angles, and one angle measures 74 degrees, what is the measure of the angle vertical to it?
74 degrees
A dilation with a scale factor of k = 1/2 is performed on a polygon. Is the resulting image congruent, similar, or both, to the original polygon?
Similar Only
A rectangle has a width of 9 meters and a diagonal of 15 meters. What is the length of the rectangle?
12 meters
Which transformation changes the size of a geometric figure but keeps its shape identical?
Dilation
If a cone and a cylinder have the exact same radius and height, how many times greater is the volume of the cylinder compared to the cone?
3 times greater
Lines L1 and L2 are parallel and cut by a transversal. If angle 1 and angle 2 are alternate interior angles, and angle 1 = 2x + 10 and angle 2 = 3x - 15, what is the value of x?
X=25
Triangle MNO has side lengths of 5, 12, and 13. Triangle PQR has side lengths of 10, 24, and 26. Are these two triangles congruent or similar?
Similar