Lines, Line Segments, and Rays
Which geometric figure starts at a specific point and extends infinitely in only one direction?
Ray
Which of the following statements represents a fundamental postulate in geometry regarding points and lines?
A. A line contains at least 3 points.
B. Through any two points, there is exactly one line.
C. Three points are always collinear.
D. A plane contains exactly one line.
B. Through any two points, there is exactly one line.
Which postulate determines what geometric figure is formed when two distinct, non-parallel planes intersect each other?
Intersection of Planes Postulate
Point B lies on a line segment between endpoints A and C. If the length of segment AB is 5 units and the length of segment BC is 8 units, what is the length of segment AC?
13 units
Consider points X and Y on a straight line. If a geometric figure starts at point Y and goes infinitely in the direction of point X, how is it correctly named?
Ray YX
If two distinct planes intersect, what kind of geometric figure is formed by their intersection?
A line
If two distinct planes intersect, how many points do the two planes share along their intersection?
Infinitely many points
Point M is between points L and N on a straight line. The total distance from L to N is 24 centimeters. If the length of segment LM is 9 centimeters, what is the length of segment MN?
15 centimeters
How many points of intersection must two distinct, non-parallel straight lines share?
Exactly one point
What is the minimum number of non-collinear points needed to determine a unique plane?
3
Think about a standard rectangular cardboard box. The flat top surface (the top plane) and the flat front surface (the front plane) intersect. What is this line of intersection called?
An edge
Points P, Q, and R are collinear, with Q lying between P and R. The lengths are given as PQ = 2x, QR = 3x + 4, and the total length PR = 29. What is the length of segment QR?
19 units
On a single straight line, points A, B, and C are in that exact order (A is on the left, B is in the middle, C is on the right). How many unique line segments can be named using these three points as endpoints?
3 (AB, BC, AC)
In a plane, if two distinct lines are both perpendicular to the same line, what must be true about those two lines?
BONUS: What is this theorem?
They are parallel to each other.
BONUS: Converse of Perpendicular Transversal Theorem
Imagine you have three different planes that all intersect. If no two of these planes are parallel, what is the maximum number of lines of intersection that can be formed?
3
Points (X), (Y), and (Z) are collinear, with (Y) lying strictly between (X) and (Z). The length of XY is represented by x2 - 3x. The length of YZ is represented by the expression 4x + 6. The total length of the entire segment XZ is 20 units.
What is the length of segment XY?
0.88 units
Imagine a standard 2D coordinate plane. Line L passes through the origin (0,0) and extends infinitely in both directions.
Imagine a standard 2D coordinate plane. Line L passes through the origin (0,0) and extends infinitely in both directions. [1, 2, 3]
If you place two points at the origin (0,0) and (2,2), how many distinct rays have you created on line L?
Imagine 4 non-coplanar points in space, like the vertices of a tetrahedron (a 3D shape like a pyramid with a triangular base). If you choose any 3 of these points, they determine a unique plane. How many unique planes can be formed by these 4 points?
4 planes
Imagine a perfect cube. If you pass an infinite flat plane directly through the center of the cube, slicing it at an angle so that it cuts through all six faces of the cube, what 2D geometric shape does the exposed cut surface (the cross-section) form?
A regular hexagon
A long wooden board has four markings on it in order: (P), (Q), (R), and (S). You know the following measurements:
What is the total length of the board from P to S?
14.4 inches.