Geometry Class Exercise 1
2014 Fall
MASSBCLS Grade 7
Basic Concepts
Line Related Teminologies
 Points: In geometry, we use points to specify exact locations. They are generally denoted by a number or letter. Because points
specify a single, exact location, they are zero-dimensional. In other words, points have no length, width, or height. It may be
helpful to think of a point as a miniscule "dot" on a piece of paper.
Lines: A line is one-dimensional, having length, but no width or height. Lines are uniquely determined by two points. We
denote the name of a line passing through the points A and B as
, where the two-headed arrow signifies that the line passes
through those unique points and extends infinitely in both directions.
Line Segments: A segment of a line that begins somewhere and ends somewhere. The name of a line segment with endpoints A
and B as
.
Rays: A ray is a "straight" line that begins at a certain point and extends infinitely in one direction. It has one endpoint. A ray
beginning at the point A that passes through point B is denoted as
.
Endpoints: Endpoints mark the beginning or end of a line segment or ray. Line segments have two endpoints, giving them
defined lengths, whereas rays only have one endpoint, so the length of a ray cannot be measured.
Midpoints: The midpoint of a line segment marks the point at which the segment is divided into two equal segments. If M is
the midpoint of the segment
, then
. Neither lines nor rays can have midpoints because they extend infinitely in
at least one direction
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Relation between Lines

Intersection: When we have lines, line segments, or rays that meet, or cross at a certain point, we call it an intersection point.
In other words, those figures intersect somewhere.
Parallel: Two lines that will never intersect are called parallel lines. In the case of line segments and rays, we must consider the
lines that they lie in. If the lines they lie on never intersect, they are called parallel. The statement "
is parallel to
," is
expressed mathematically as
.
Transversal: A transversal is a type of line that intersects at least two other lines. The lines that a transversal crosses may or
may not be parallel.
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Misc

Planes: A plane can be thought of as a two-dimensional flat surface, having length and width, but no height. A plane extends
indefinitely on all sides and is composed of an infinite number of points and lines. One way to think about a plane is as a sheet
of paper with infinite length and width.
Space: Space is the set of all possible points on an infinite number of planes. Thus, space covers all three dimensions - length,
width, and height.
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Line Related Concept Practices
1. AB = 8cm. C is a point on AB. M is the midpoint of AC, N is the midpoint of CB. MN = 3cm
2. A, B, C are three points on line 𝑙. AB = 9cm, BC=4cm. O is the midpoint of AC, OA = 6.5cm
Fly a) Draw the shortest path for the Spider to get to the Fly
3.
b) If the Spider must craw along the edge of the cube, what are the shortest paths the Spider can
take?
Spider
4. A shuttle bus needs to pick up passengers from three buildings on the same line: Building A, B and C. Building A has 30 people
to take this bus. Building B has 15 people to take this bus. Building C has 10 people to take this bus. If the bus only stops at one
place for all passengers to get on, which of the following places will have minimum total walking distance from all passengers?
200
100
A
B
C
A) Building A
B) Building B
C) Building C
D) Between Building A and B
5. Find the length of the 24th segment in the graph:
Answer: 12
6. A1 and A2 are on line 𝑙. How many rays and line segments can be defined with these two points? 4 rays, 1 segment
A1, A2 and A3 are on line 𝑙. How many rays and line segments can be defined with these three points? 6 rays, 3 segments
A1, A2 …An are on line 𝑙. How many rays and line segments can be defined with these n points? 2n rays, n(n-1)/2 segments