Geometry Unit 1

Name the ordered pair indicated by point B on the coordinate plane.

(-3,1)

Name the ordered pair indicated by point C on the coordinate plane.

(-5,-2)

Name the ordered pair indicated by point D on the coordinate plane.

(3,-3)

Name the ordered pair indicated by point A on the coordinate plane.

(4,2)

Using the given coordinates and the Ruler Postulate, calculate the length of the line segment DF—

1

Using the given coordinates and the Ruler Postulate, calculate the length of the line segment FI—

1 1/2 or 1.5

Calculate the length of segment AB— with midpoint, M , if AM— =5.

10

Using the given coordinates and the Ruler Postulate, calculate the length of the line segment DH—

2

Calculate the length of segment RS— with midpoint, M , if RM—=5x and MS—=x+12.

30

Carlos drove two friends home after their school's football game. Gene's house (G) is 10 miles from the school (F) and Hector's house (H) is 14 miles from the school. How far must Carlos drive from Gene's house to Hector's house?

4 Miles

How many points are on this plane?

6

If AY—=4 , what is the measure of AC— ?

8

Which angle has a measure less than 90 degrees?

A

Which angle is an acute angle?

A

Which choice names an endpoint?

A

Which choice names a line segment?

AB—

Name two line segments that have the same length. _____ and _____.

AY—; YC—

Which of these statements is NOT one of Euclid's axioms?

All angles are equal to each other.

_____ a universally accepted principle which does not require proof.

Axiom

Which angle has a measure greater than 90 but less than 180 degrees?

B

Select SIX possible line segments.

BA—; CA—; CB—; BC—; AC—; AB—

Which choice names a ray?

BC→

Select SIX possible rays.

BC→; BA→; AB→; CA→;CB→; AC→

Name the line.

BC↔; AB↔; BA↔; CA↔; AC↔; CB↔

Which is a right angle?

C

Which angle has a measure of 180 degrees?

D

_____ uses calculus to study how geometric functions respond to changing variables.

Differential geometry

A Greek mathematician and teacher named ___________________ who lived in the 3rd century BC, established the basis for geometry in a set of axioms.

Euclid

_____ based on the axioms of Euclid.

Euclidean geometry

Identify the postulate illustrated by the statement: Line ST↔ connects point S and point T .

Postulate 1.2A: Through any two points there is exactly one line.

Which postulate explains why I-30 is the only way to get from Dallas to Fort Worth?

Postulate 1.2A: Through any two points there is exactly one line.

To pass Geometry, you should: Read everything carefully, including the text, boxes, side notes, and __________. Since one concept, diagram, or statement might look like another, you need to pay attention to __________. Make sure you understand each __________ before you go on to the next. If you don't understand something, __________ it again. If that doesn't work, ask for help. Before you begin each Lesson, take a few minutes to __________ the material in the previous Lesson.

To pass Geometry, you should: captions details concept read review

True or False: A postulate is accepted as true without proof.

True

Which line is a segment bisector?

XZ↔

Which point is the midpoint of a line segment?

Y

Which of the following statements is NOT a reasonable statement about geometry?

You need to take geometry so you will learn how to drive farther and faster.

Which is the best definition for angle?

a figure formed by two rays with a common endpoint

Which is the best definition for the term "segment bisector"?

a line, line segment, or ray that intersects a line segment at its midpoint

Which is the best definition for the term "construction"?

a method of creating a geometric figure that is mathematically precise by using a compass and straightedge

Which is the best definition for the term "coordinate"?

a number that corresponds to a point

Which is the best definition for coordinate plane?

a plane that is divided into four regions by a horizontal line, called the x-axis, and a vertical line, called the y-axis

Which is the best definition for the term "midpoint"?

a point that bisects a segment into two congruent segments

Which is the best definition for angle bisector?

a ray that bisects an angle into two congruent angles

Which three points are collinear?

a; b; c

Which points are coplanar?

a; b; c; d; e; f

If three points A , B , and C are _____ , and B is between A and C , then AB+BC=AC . (the Segment Addition Postulate)

collinear

Which three points are noncollinear?

d; e; f

A point is a location in space that has neither size nor _____.

dimension

A property of space consisting of the measure of distance in one direction is called ___.

dimension

Which is the best definition for the term "bisect"?

dividing into two equal or congruent parts

The point at either end of a line segment or the point at the start of a ray is the ___.

endpoint

True or False: Points that lie on the same plane are collinear.

false

True or False: Solid geometry deals with two-dimensional objects.

false

Which is the best definition for the term "congruent"?

having the same size and shape

A straight path that has no thickness and extends forever is a ___.

line

If two planes intersect, they intersect in exactly one ______________. (Postulate 1.2E)

line

Points that lie on the same ___ are collinear points.

line

Through any two points there is exactly one ________________________. (Postulate 1.2A)

line

A ___ consists of two endpoints and all the points in between them.

line segment

A portion of a line consisting of two points and all the points between them is called a(n) ___.

line segment

If any two points lie on a plane, then the __________ that contains those two points also lies on the __________. (Postulate 1.2C)

line; plane

Through any three __________ __________ there is exactly one plane.

noncollinear points

What is the best definition for quadrant?

one of four regions into which a coordinate plane is divided

The points on any line or line segment can be put into a __________ correspondence with real numbers so that two selected points can have coordinates 0 and 1, and that the distance between two points is the ___________value of the difference between the corresponding numbers. (the Ruler Postulate)

one-to-one; absolute

A ___ is a flat surface that has no thickness and extends forever.

plane

Points that lie on the same ___ are coplanar points.

plane

A location in space, called a ___, has no size or dimension.

point

If two lines intersect, they intersect at exactly one ____________________. (Postulate 1.2D)

point

A(n) ___ is a statement accepted as true without proof as a basis for reasoning.

postulate

Which is the best definition for the interior of an angle?

the set of points between the two sides of an angle

Which is the best definition for the exterior of an angle?

the set of points outside an angle

A plane is a flat surface that has no ___ and extends forever.

thickness

True or False: Euclidean Geometry is based on the postulates of Euclid.

true

True or False: Plane geometry deals with two-dimensional objects.

true

True or False: Points that lie on the same line are collinear.

true

Terms that describe basic geometric figures that are fundamental to all other geometric figures and, as such, cannot be defined by using other geometric terms are called ___.

undefined terms

_____ the branch of mathematics that deals with the study of geometric figures, such as points, lines, planes, and solids, and the deduction of properties, measurements, and relationships of those figures.

Geometry

In order to take this course, you will need these tools: a center-wheel __________ for drawing circles and arcs a clear __________ for measuring angles a __________ for drawing straight lines a graphing __________ and a computer with geometry software a copy of the __________ __________ __________ with a list of the definitions, properties, postulates, theorems, and corollaries that you will need for writing proofs

In order to take this course, you will need these tools: compass protractor straightedge calculator Geometry Proof Manual~

Using the midpoint and distance formulas, calculate the coordinate of the midpoint and the length of the segment AB—.

Length of Segment AB— : 5 Coordinates of Midpoint: (2.5,3)

Using the midpoint and distance formulas, calculate the coordinate of the midpoint and the length of the segment RS—.

Length of Segment RS— : √8 Coordinates of Midpoint: (2,2)

Geometry involves concepts that are abstract. According to the definition in the text, which sentence below best uses the word abstract?

Patriotism is a strong emotion, but it is still an abstract concept.

Select THREE possible names for the plane.

Plane ABD; Plane 𝓡; Plane BCE

_____ deals with two-dimensional objects, such as squares and circles.

Plane geometry

Identify the postulate illustrated by the statement: If the line LM↔ intersects line MO↔ , points L,M, and O are all on the same plane.

Postulate 1.2B: Through any three noncollinear points there is exactly one plane.

Which postulate tells why Dallas, Fort Worth, and Denton are not in any other plane but Texas?

Postulate 1.2B: Through any three noncollinear points there is exactly one plane.

Identify the postulate illustrated by the statement: Point F and point G lie on plane R, so line FG↔ lies on plane R.

Postulate 1.2C: If two points lie on a plane, then the line that contains those two points also lies on the plane.

Which postulate tells why I-30 lies on the plane of Texas?

Postulate 1.2C: If two points lie on a plane, then the line that contains those two points also lies on the plane.

Identify the postulate illustrated by the statement: Line AB↔ and line CD↔ intersect at point P.

Postulate 1.2D: If two lines intersect, they intersect at exactly one point.

Which postulate tells why I-30 and I-35W intersect only at Fort Worth?

Postulate 1.2D: If two lines intersect, they intersect at exactly one point.

Identify the postulate illustrated by the statement: Plane J and plane K intersect at line JK↔.

Postulate 1.2E: If two planes intersect, they intersect in exactly one line.

Which postulate is illustrated by the place where the two walls meet in the photo on the right?

Postulate 1.2E: If two planes intersect, they intersect in exactly one line.

_____ deals with three-dimensional objects, such as cubes and spheres.

Solid geometry

___ is the unlimited region in which all things exist.

Space

A ___ is a part of a line that has one endpoint and extends in only direction forever.

ray

A(n) ___ is a portion of a line that starts at one point and extends forever in only one direction.

ray

An endpoint is at both ends of a line _____ or at the start of a ray.

segment

A line is a _____ path that has no thickness and extends forever.

straight

Which is the best definition for vertex?

the common endpoint of the rays of an angle

What is the best definition for the origin?

the point where the x-axis and the y-axis intersect on a coordinate plane

What is the best definition for an ordered pair?

the set of coordinates that indicates the position of a point on a coordinate plane