Geometry Basics
What geometric figure extends forever in both directions and has no endpoints?
A line
A(4,6) is translated 5 units left and 3 units down. What are the coordinates of A′?
A′ (−1,3)
Two angles that are directly across from each other at the same intersection are called what?
Vertical angles
What type of triangle has three congruent sides?
Equilateral triangle
In Experiment 1, a coin lands on tails 6 times out of 10 flips. In Experiment 2, the coin lands on tails 5 times out of 10 flips. When the two experiments are combined, what is the experimental probability of landing on tails?
P = 11/20 = 55%
What is the difference between a line segment and a ray?
A line segment has two endpoints; a ray has one endpoint and extends forever in one direction.
Point B(-3,7) is reflected across the y-axis. What are the coordinates of B′?
B′(3,7)
When parallel lines are cut by a transversal, are corresponding angles congruent or supplementary?
Congruent
A triangle has angle measures 35∘ 55∘, and 90∘. Classify it by angles (what type of triangle is it?)
Right triangle
A fair six-sided die is rolled once. What is the theoretical probability of rolling a number greater than 4?
P = 1/3
Points A, B, and C lie on the same straight line. What word describes these points?
Collinear
Point C(5,−2) is rotated 90 degrees clockwise about the origin. What are the coordinates of C′?
C′(−2,−5)
When parallel lines are cut by a transversal, what relationship exists between same-side interior angles?
Supplementary
The three interior angles of a triangle measure 2x+14, 3x−6, and x+10. Find x and all three angle measures.
x=27; 68∘, 75∘, 37∘
A point is randomly chosen on a 30-unit line segment. A favorable portion of the segment is 12 units long. What is the probability of landing in the favorable portion?
P = 2/5
Find the midpoint between (−6,4) and (8,10)
(1,7)
Point D(−4,3) is translated 6 units right and 5 units down. The new point is then reflected across the x-axis. What are the final coordinates of D′′?
D′′(2,2)
Corresponding angles have measures 4x+18 and 6x−14. Find x.
x=16
The two remote interior angles of a triangle are 53∘ and 72∘ Find the exterior angle.
125∘
A point is randomly chosen inside a 10×8 rectangle. A right triangular target inside it has a base of 6 and height of 4. What is the probability of landing inside the triangle?
P(triangle) = 3/20
What is the distance between (7,9) and (−4,−3)? Give your answer in simplest radical form.
Square Root : 265
Point E(6,-2) is reflected across y = −x. The image is then rotated 270 degrees counterclockwise about the origin. What are the final coordinates of E′′?
E′′(−6,−2)
Two same-side interior angles measure 3x+24 and 5x−4. Find x and both angle measures.
x=20; 84 degrees and 96 degrees
An isosceles triangle has a vertex angle of 48∘. Each base angle measures 1/2x + 12. Find x.
x=108
A point is randomly chosen inside a rectangular prism measuring 10×8×6. A target rectangular prism inside it measures 4×3×2. What is the probability of landing inside the target volume?
P = 1/20