Geometry MSE2183 Mathematics 218 Assignment TWO of 2022.
Explanations and diagrams are used for elaboration.
Definitions using the three building blocks of Geometry.
Identify/create line segments, collinear and coplanar points.
Naming lines.
Midpoints of diagonals of parallelograms.
The Van H...
The three building blocks of Geometry adapted from the MSE2183 Study Guide:
(a) A point is the most basic building block of geometry. It has only one location, has
no size and can be represented by a dot.
(b) A line is a straight arrangement of indefinitely many points, it extends continuously
in two directions, it has no thickness, it has infinite length.
(c) A plane is a flat surface, it is indefinitely large, has zero thickness, has length and
width, represented by a four-sided figure, it looks like a tilted paper.
A ray is a straight arrangement of indefinitely many points, it extends continuously in one direction,
it has no thickness, and it has infinite length. A ray is a special type of a line, and it is represented by
having a point on one end and an arrow on the other end.
Two or more points are said to be collinear if they lie on the same line.
Points 𝐸, 𝐹 and 𝐻 are collinear.
Points 𝐼 and 𝐿 are collinear.
Two or more points are said to be coplanar if they lie on the same plane.
The four black points, 𝑂, 𝑃, 𝑄 and 𝑅 are coplanar.
, A line segment is a straight arrangement of indefinitely many points. It starts from one fixed point
and ends on another fixed point. The two fixed points are called endpoints. A line segment has finite
length.
Line segments are congruent if they have the same length.
Line segment ̅̅̅̅
𝐴𝐵 is congruent to line segment ̅̅̅̅
𝐶𝐷. Both segments have a length of 10 centimetres.
If two or more lines pass through the same point, then they are said to be concurrent.
⃡ and 𝐿𝑀
Lines 𝐽𝐾 ⃡ are concurrent at point 𝐼.
The midpoint of a line segment is the point on the segment that is the same distance from both
endpoints. The midpoint divides the original line segment into two congruent line segments.
The point 𝑁 is the midpoint of line segment 𝐿𝑀.
For two of more lines, if such lines cross each other at some single point, then they are said to be
intersecting lines.
Lines ⃡𝐽𝐾 and ⃡𝐿𝑀 are intersect at point 𝐼.
A point or a line bisects a line segment if the point/line divides the line segment into two congruent
line segments.
Line ⃡𝐽𝐾 bisects line segment ̅̅̅̅
𝐿𝑀.
Point 𝑁 bisects line segment ̅̅̅̅
𝐿𝑀.
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