Points, Lines & Planes
$100: A flat surface that extends forever in all directions and has no thickness is called what?
Answer: A plane.
$100: A portion of a line with two endpoints is called what?
Answer: A segment.
$100: B is between A and C. If AB = 7 and BC = 9, find AC.
Answer: 16.
$100: Ray BD lies inside ∠ABC. If m∠ABD = 30° and m∠DBC = 25°, find m∠ABC.
Answer: 55°.
$100: Two angles have measures of 35° and 55°. What relationship do they have?
Answer: Complementary.
$200: What term describes points that lie on the same line?
Answer: Collinear.
$200: When naming a ray, which point must be written first?
Answer: The endpoint.
$200: E is between D and F. If DF = 25 and DE = 11, find EF.
Answer: 14.
$200: Ray QS lies inside ∠PQR. If m∠PQR = 100° and m∠PQS = 64°, find m∠SQR.
Answer: 36°.
$200: Two angles have measures of 118° and 62°. What relationship do they have?
Answer: Supplementary.
$300: What term describes points and lines that lie in the same plane?
Answer: Coplanar.
$300: Points A, B, and C lie in that order on the same line. Name the two rays with endpoint B.
Answer: Ray BA and ray BC.
$300: M is between L and N. If LM = 3x, MN = 8, and LN = 29, find x.
Answer: 7.
$300: Ray BD lies inside ∠ABC. If m∠ABC = 80°, m∠ABD = 3x + 5°, and m∠DBC = 2x°, find x.
Answer: 15.
$300: Two lines intersect. One angle measures 73°. What is the measure of its vertical angle?
Answer: 73°.
$400: If two lines intersect, how many points are in their intersection?
Answer: Exactly one point.
$400: Points D, E, and F are collinear with E between D and F. What special relationship exists between ray ED and ray EF?
Answer: They are opposite rays.
$400: P is between Q and R. If QP = 4x − 3, PR = 2x + 5, and QR = 32, find x.
Answer: 5.
$400: Ray BD lies inside ∠ABC. If m∠ABC = 145°, m∠ABD = 6x + 7°, and m∠DBC = 4x − 2°, find x.
Answer: 14.
$400: Two angles form a linear pair. Their measures are (3x + 10)° and (5x + 2)°. Find x.
Answer: 21.
$500: Two distinct planes intersect. What must their intersection be?
Answer: A line.
$500: Explain the difference between a line, segment, and ray using the number of endpoints.
Answer: A line has no endpoints, a segment has two endpoints, and a ray has one endpoint.
$500: A is between B and C.
BA = 5x − 7, AC = 3x + 5, and BC = 54.
Find x, BA, and AC.
Answer: x = 7; BA = 28; AC = 26.
$500: Ray BD lies inside ∠ABC.
m∠ABD = 5x + 12°
m∠DBC = 3x + 8°
m∠ABC = 132°
Find x and both smaller angle measures.
Answer: x = 14; ∠ABD = 82° and ∠DBC = 50°.
$500: Two intersecting lines create four angles. One angle measures (7x − 5)° and an adjacent angle measures (4x + 20)°. Find x and the measures of all four angles.
Answer: x = 15; the four angles are 100°, 80°, 100°, 80°.