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Math
Geometry
Geometry - 1.7 & 1.8 Review
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Terms in this set (21)
Define a midpoint.
the point on the line segment that divides it into two segments of equal lengths
If line AC = 30 and point B is the midpoint of the line segment AC, what is the measure of AB?
AB = 15
Define a segment bisector.
a line, ray, or segment that passes through the midpoint of another segment
- NOTE: the segment that is bisecting does not have to be at its midpoint! (ex: segment PQ's midpoint is F but segment AB's midpoint does not have to be F)
If segment PQ bisects segment CT at point A and AT = 10, what is the measure of segment CT?
CT = 20
Define an angle bisector.
a line, segment, or angle that divides an angle into two congruent angles
If the ray AT bisects the right angle ∠MAP, what is the measure of ∠TAP?
m∠TAP = 45º
Define perpendicular.
any two lines, segments, or rays that intersect to form directly 90º angles or right angles
- uses symbol ⊥
If ∠SAD is a right angle, could you say ray SA and ray AD are perpendicular?
yes! they meet to form a 90 degree angle
What are axioms?
basic assumptions that we make about lines
- also known as postulates
- facts that we take as being true without being able to prove or disprove them
How many straight lines can be drawn between two points?
only one
What is the shortest distance between any two points?
length of the straight line segment connecting them
Two different lines will either...
- share or intersect at one point
- share none at all
any two lines that share two or more points are the same line
Describe Euclid's Parallel Postulate.
through any point
not
on a given line, there is exactly
one
line that can be drawn parallel to the given line
Through any point on a given line, how many lines can be drawn perpendicular to it?
ONE
Through any point
not
on a given line, how many lines can be drawn perpendicular to a given line?
ONE
When a given line separates a plane into two halves, what does it make?
a half-plane
If a given line separates a plane into two halves, where do the points in the plane have to fall on?
the points in the plane either fall on
- the line
- one of the half-planes
If a given line separates the plane into two halves, how can you tell if two points are on opposite halves of the plane?
if the segment connecting them intersects the given line
What is a plane?
a flat surface that extends without end and has no thickness
- consists of infinitely many lines
- ex: coordinate plane, picture
One of the axioms are that a segment connecting two points on opposite sides of a given line must intersect that line. Is it always true that a line connecting two points on the
same
side of a given line will be parallel to that given line?
no! a line that connects two points on a singular side of a half-plane can intersect and pass the given line
How do you know if two lines that are not parallel to each other will intersect on the left or the right of a transversal line?
add up the angles on both sides of the transversal and see which one is less
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