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Math
Geometry
Geometry - Unit 1 Review
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Unit 1: Foundations (1.1-1.5, 1.7-1.8)
Terms in this set (49)
Define a point.
a location with no size and is undefined
Define distance.
the length of a line segment that connects two points
Define axiom.
a statement that is accepted as being true without any proof
Define a line segment.
shortest path or length between two points
- part of a line that consists of two endpoints and all of the points in between
- ex: AB or AB with a - on top
Define collinear.
points that lie on the same line
- ex: AB + BC = AC
Define a line.
a straight path that extends in two opposite directions forever and has no thickness
- ex: AB with a <-> on top of the letters
Define a ray.
part of line that consists of one endpoint and all of the points on the line are on one side of that endpoint
- ex: AB with -> on top
Why can you measure a line segment but not a line?
line segment has a start and stop while a line has no end
Define angle.
formed by two rays with the same endpoint
- rays are the side and the endpoint is the vertex (turning point)
- symbolized by ∠ (ex: ∠ABC)
- note: make sure vertex is always the middle letter when naming the angle!
If ray BC separates ∠DBA into two parts, find the numerical value of m∠DBA if m∠CBA = x + 7, m∠DBC = 48º, and m∠DBA = 4x - 20.
m∠DBA = 80º
What is an acute angle?
an angle that is less than 90º and more than 0º
What is an obtuse angle?
an angle that is more than 90º and less than 180º
What is a right angle?
an angle that is exactly 90º
What is a straight angle?
an angle that is exactly 180º
What is a reflex angle?
an angle that is greater than 180º
If ∠BAM is a right angle and m∠BAM = 4x + 22, solve for the value of x.
x = 17
Define a complementary angle.
two angles with a sum of 90º
Define a supplementary angle.
two angles with a sum of 180º
If m∠BAC = 40º, what would be the measure of an angle that is complementary to it and the measure of an angle that is supplementary to it?
complementary = 50º
supplementary = 150º
It is given that ∠A and ∠B are complementary. If the measure of ∠B is 15 more than twice than the measure of ∠A, determine the measure of both angles algebraically.
m∠A = 25º
m∠B = 65º
The measure of two supplementary angles, ∠S and ∠T, are in the ratio of 7:3. Find the value of m∠S.
m∠S = 126º
If ∠TAP and ∠BRE are supplementary and ∠BRE is its own complement, find the measure of ∠TAP.
m∠TAP = 135º
Define vertical angles.
angles that are opposite of each other when two straight lines cross & that have the same measure
Define a circle.
the set of all points equidistant to one point (center) in 2D space
- ex: ◯ A
Define equidistant.
when all points are the same distance from another point (apparent in circles)
If points C and D lie on the perimeters of circle O, find the length of the radius of circle O if OC = 6x + 2 and OD = 10x - 16.
29
What is triangle notation?
Define a midpoint.
the point on a
line segment
that divides it into two segments of equal lengths
Define a segment bisector.
a line, ray, or segment that passes through the midpoint of another segment to divide it into two equal parts
Define an angle bisector.
a line, segment, or angle that divides an angle into two congruent angles (two angles with the same measure)
Define perpendicular.
any two lines, segments, or rays that intersect to form directly 90º angles or right angles
- symbolized by ⊥ (AB ⊥ BD)
If point C was the midpoint of AB, D was the midpoint of BC, and E was the midpoint of CD, find the length of AB if mED = 5.
mAB = 40
If line DE bisects line AB at point C, is point C the midpoint of AB, DE, or both?
only AB — unless given further knowledge, the line that is bisecting does not have to be at its midpoint
It is known that ray AP bisects angle ∠CAT. If m∠CAT = 5x + 17 and m∠PAT = 3x - 4, then determine the value of x.
x = 25
M is the midpoint of the line segment PQ. If PM = 5x + 8 and PQ = 76, find the value of x.
x = 6
Through any two points...
only one straight line can be drawn
The shortest distance between any two points is comprised of...
the length of the straight line segment connecting them
Two different lines will either...
share (intersect) at one point or share none at all (parallel lines)
- any two lines that share two or more points are the same line
What is 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
- also phrased as two straight lines that are crossed by a transversal will be only parallel if the sum of the two interior angles formed on the same side of the transversal is equivalent to the sum of two right angles
How many lines can be drawn perpendicular through any point on a given line?
exactly one line can be drawn perpendicular to the given line
How many lines can be drawn perpendicular to a given line through any point not on the given line?
exactly one line can be drawn perpendicular to the given line
Define a plane. What are some examples?
a flat surface that extends without end and has no thickness
- consists of infinitely many lines
- ex: coordinate plane, photo
Define a half-plane.
half of a plane formed when a given line separates the plane into two halves
If a given line separates a plane into two halves, any point on the plane has to lie...
one of the half-planes or one line
How do you know if two points are on opposite sides of a plane?
if the segment connecting them intersects the given line that separates the plane
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 - line may intersect the given line
Can you determine a way to know on which side of a transversal two non-parallel lines will intersect?
the side of the transversal with the lesser sum of the interior angles formed will be the side the lines intersect
Segment AB intersects segment CD at E. If AB is the perpendicular bisector of CD, then which of the following does not have to be true?
1) CE ⊥ AD
2) CD = 2(DE)
3) CE + EB = DE + EA
4) AE + EB = AB
3) CE + EB = DE + EA
Which of the following statements is not true?
1) Every angle has only one unique line that bisects it.
2) Every segment has only one unique line that bisects it.
3) Through any point not on a line, there is only one line that can be drawn through the point parallel to it.
4) Through any point not on a given line, there is only one line that can be drawn through the point perpendicular to the first line.
2) Every segment has only one unique line that bisects it.
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