Points, Lines, and Planes
Explain whether three points always determine a plane.
What is it does not always determine a plane, it must be three non-collinear points for it to form a plane?
Find the midpoint of AB if A is at -5 and B is at 15.
What is 5?
Coplanar lines that do not intersect.
What are parallel lines?
If a transversal intersects two parallel lines, then same-side interior angles are (congruent/supplementary).
What is supplementary?
Undefined terms in Euclidean Geometry
B is the midpoint of AC. Find x if AB=3x and BC=5x-6.
What is x=3?
Noncoplanar lines that are not parallel and do not intersect.
What are skew lines?
∠1 and ∠2 are same-side interior angles formed by two parallel lines and a
transversal. Find m∠2 if m∠1 = 115.
What is 65?
A part of a line that consists of two endpoints and all points between them.
What is a segment?
Angles with the same measure.
What is congruent angles?
An angle supplementary to 67.
What is 113?
∠1 and ∠2 are vertical angles. Find the value of x if m∠1 = 4x and m∠2 = 56.
What is x=14?
A part of a line that consists of one endpoint and all the points of the line on one side of the endpoint.
What is a ray?
Find the angle measure of the hands of a clock at 6:00.
Nonadjacent interior angles that lie on opposite sides of a transversal.
What are alternate interior angles?
People in ancient Rome played a game called terni lapilli. The exact rules of this game are not known. Etchings on floors and walls in Rome suggest that the game required a grid of two intersecting pairs of parallel lines, similar to the modern game tick-tack-toe. The measure of one of the angles formed by the intersecting lines is 90°. Find the measure of each of the other 15 angles. Justify your answers.
What is 90?