Geometry A

Use the graph of figure ABCD and its image, figure A′B′C′D′, to answer the question. © 2016 StrongMind. Created using GeoGebra. Long Description: Image of Figure The transformation takes each point (x,y) to a new coordinate (x′,y′). Which function correctly describes the transformation?

(x,y)↦(−x,y) lesson 6

hypothesis

the part of a conditional statement that follows the word "if" (noun)

coplanar

lying on the same plane (adjective)

symmetry

a property of a figure in which the image coincides with the preimage after certain rigid transformations (noun)

LESSON 10

LESSON 10

congruent angles

angles that have equal measures (noun)

LESSON 1

LESSON 1

center of symmetry

a point about which a preimage is rotated by an angle so that the image coincides with the preimage; also known as point of symmetry (noun)

line symmetry

a type of symmetry in which a figure is reflected over a line so that the image coincides with the preimage; also known as reflection symmetry (noun)

point

an exact location, represented by a dot, that has no size (noun)

perpendicular bisector

a segment bisector that intersects the line segment at a 90∘ angle (noun)

Select two of the following mapping statements that are the result of the same translation.

(2,−3)↦(5,−8) (−1,2)↦(2,−3) lesson 6

corresponding angles

angles in the same relative position in two different polygons (noun)

superimpose

to place one figure on top of another (verb)

What must be true in order for two lines to be parallel? There is more than one correct answer. Select all that apply lesson 1

The lines must never intersect. The lines must be in the same plane. lesson 1

equidistant

having equal distances (adjective)

parallel lines

two or more coplanar lines that never intersect (noun)

congruent

having the same size and shape (adjective)

origin

the point (0,0) on the coordinate plane (noun)

What notation is used to represent the distance from point A to B? lesson 1

AB lesson 1

What is the definition of perpendicular lines? lesson 1

Perpendicular lines are two lines that intersect to form four congruent right angles. lesson 1

preimage

a figure before a transformation is applied (noun)

Which statement is correctly written as a conditional statement?

If four is a perfect square, then you can evaluate its square root. lesson 4

counterclockwise

In a direction opposite to the movement of the hands on a clock's dial (adverb)

LESSON 4

LESSON 4

LESSON 5

LESSON 5

output

a value that results from putting an input into a relation (noun)

clockwise

in the direction in which the hands of a clock turn (adverb)

LESSON 6

LESSON 6

transformation

a change in the size, shape, or position of a figure in a plane (noun)

Vocabulary (day 2) angle

a figure formed by joining two rays at their initial points (noun)

plane

a flat surface, consisting of length and width but no depth, that continues forever in two directions (noun)

segment bisector

a line, ray, or segment that divides a line segment into two congruent segments (noun)

KEY TERMS angle bisector

a line, ray, or segment that passes through the vertex of an angle and divides the angle into two congruent angles (noun)

translation

a rigid transformation that maps each point in a figure the same distance in the same direction (noun)

rigid transformation

a transformation that preserves side lengths and angle measures Transformations are translations, reflections, and rotations are rigid transformations. (noun)

KEY TERMS: angle of rotational symmetry

the smallest angle by which a figure can be rotated about a point so that the image coincides with the preimage (noun)

corresponding sides

sides in the same relative position in two different polygons (noun)

perpendicular lines

two lines that intersect to form a right angle (noun)

What does the statement "a logical argument written with statements in one column and the corresponding reason in another column" define?

two-column proof lesson 5

midpoint

a point that bisects a segment (noun)

center

a single point that is the same distance from every point on a circle or sphere (noun)

included angle

an angle between any two adjacent sides of a polygon In △ABC, ∠B is included by AB¯¯¯¯¯¯¯¯ and BC¯¯¯¯¯¯¯ (noun)

What term does the statement "a figure formed by two rays that share a common point" define?

angle lesson 2

What term does the statement "the set of all points in a plane that are equidistant from a given point" define?

circle lesson 2

KEY TERMS bisect

to cut an object into two congruent parts (verb)

proof

an organized, logical way of presenting a list of facts that leads to a conclusion (noun)

Draw a line. Now draw a line perpendicular to the first line that passes through point G (which is not at the intersection). Measure the distance of G from the first line. Draw another point on the second line that is the same distance as G, but is on the opposite side of the first line. If G is the preimage, and the second point is the image, what transformation does this show?

reflection lesson 6

between (keys terms)

three collinear points such that the distance from the first to the second point plus the distance from the second to the third point is equal to the distance from the first to the third point (adverb)

Use the conditional statement to answer the question. If a rectangle is a square, then it has four congruent sides. What is the converse of the given conditional statement?

If a rectangle has four congruent sides, then it is a square. checkpoint 4

Use the following information to answer the question. One statement in a proof says, If AB=CD and CD=EF, then AB=EF. What reason can be used for the statement?

Transitive Property of Equality lesson 5

endpoint

a point that denotes the start or end of a line segment (noun)

rotational symmetry

a type of symmetry in which a figure is rotated about a point by an angle greater than 0∘ and less than 360∘ so that the image coincides with the preimage (noun)

Use the number line to complete the sentence. © 2016 StrongMind. Created using GeoGebra. The distance from point A to point B is _[blank]_ units. lesson 1

5 lesson 1

map

to move a point or set of points by using a transformation The image is the result of mapping a figure called the preimage to a new location. (verb)

translate

to shift or slide every point in a figure the same distance in the same direction (verb)

line of reflection

a line over which a figure is reflected (noun)

linear pair

a pair of adjacent angles whose noncommon sides form a straight angle (noun)

supplementary angles

a pair of angles whose measures have a sum of 180∘ (noun)

two-column proof

a proof given as specific statements and their supporting reasons in a table format (noun)

function

a relation between two quantities that has exactly one output value for each input value (noun)

A protractor is used on an angle. One ray of the angle is at 13∘ and the other ray is at 57∘. What is the measure of the angle?

44∘ lesson 2

Use the following figure to help you complete the sentence. point A -2 point B 3 © 2016 StrongMind. Created using GeoGebra. The distance between point A and point B is _[blank]_ units. Enter your answer as the number that correctly fills in the blank in the previous sentence.

5

Which of the following statements is biconditional?

A number is an even number if and only if it is divisible by 2. lesson 4

Use the definition of a parallelogram to complete the biconditional statement. A parallelogram is a quadrilateral with two pairs of parallel sides. A quadrilateral is a parallelogram _[blank]_. Which answer correctly fills in the blank in the previous sentence?

if and only if it has two pairs of parallel sides checkpoint 4

KEY TERMS coincide

to be located in the same exact place so that one figure lies directly on top of the other (verb)

vertical angles

a pair of nonadjacent angles whose sides are opposite rays (noun)

What term does the description "two lines that intersect to form four congruent right angles" define?

perpendicular lines checkpoint 1

Use the image to help you complete this problem. © 2019 StrongMind. Created using GeoGebra. Match each figure with the correct term.

point: B line: AC plane: P checkpoint 1

angle of rotation (key terms)

the angle by which a figure is rotated counterclockwise or clockwise about a fixed point (noun)

In the following graph, triangle ABC has been transformed in three different ways, resulting in triangle DEF,, triangle GHI, and triangle JKL.

1. DEF: rotation 2. GHI: translation 3. JKL: reflection lesson 6

LESSON 7

LESSON 7

LESSON 8

LESSON 8

rotation

a rigid transformation such that each point and its image are equidistant from a specific point, called the center of rotation (noun)

collinear

lying on the same line (adjective)

vertex

the point where two rays, or sides, of an angle meet (noun)

coincide

to be located in the same exact place so that one figure lies directly on top of the other (verb)

The following transformation maps △ABC△ABC to △A′B′C′.△A′B′C′.(x,y)↦(x−4,y+1)(x,y)↦(x−4,y+1)Which answer correctly describes the transformation applied to △ABC?

△ABC is moved 4 units left and 1 unit up to create △A′B′C′. lesson 6

Let pp be the statement "I do my chores," and let qq be the statement "I get my allowance." Which statement uses pp as the hypotheses and qq as the conclusion?

If I do my chores, then I get my allowance. lesson 4

Use the conditional statement to answer the question. If a polygon has three sides, then it is a triangle. What is the converse of the given conditional statement?

If a polygon is a triangle, then it has three sides. lesson 4

reflection

a rigid transformation that maps every point in the preimage to points that are equidistant from, but on the opposite side of, a line (noun)

Match each type of transformation with the correct description of that transformation. 1. rotation 2. translation 3. reflection

1. The distance between the center of rotation and a point in the preimage is the same as the distance between the center of rotation and the corresponding point on the image. 2. Every point in the preimage is mapped the same distance and direction to the image. 3. Every point in the preimage is mapped the same distance from the line of reflection to the image. lesson 6

conditional statement key terms

a statement written in the form "If p, then q" and denoted as p⇒q (Noun)

conditional statement

a statement written in the form "If p, then q" and denoted as p⇒q (noun)

biconditional statement (key terms)

a statement written in the form "p if and only if q" and denoted as p⇔q (Noun)

image

a copy of an object formed by reflected or refracted rays of light (noun)

congruence statement

a geometric statement that indicates two figures are congruent (noun)

mapping statement

a mathematical statement that uses coordinates to describe the way points are transformed The point (x,y) is used to represent any point in the image, a right arrow indicates "is mapped to," and another ordered pair shows how the coordinates of the image compare to the coordinates of the preimage. (noun)

distance

a measurement of how far apart two objects are (noun)

input

a number that is put into an expression or equation (noun)

arc

a part of a circle that consists of two endpoints on the circle and the curved section of the circle containing all the points on the circle between the two endpoints (noun)

regular polygon

a polygon with interior angles that have equal measures and sides that are equal in length (noun)

Use the graph to answer the question. © 2016 StrongMind. Created using GeoGebra. Long Description: Image of ParallelogramsWhich series of transformations correctly maps parallelogram ABCDABCD to parallelogram A′B′C′D′?A′B′C′D′?

a rotation 90∘ clockwise about the origin, followed by a translation 3 units down lesson 6

radius

a segment in a circle with one endpoint on the circle and the other endpoint at the center of the circle (noun)

LESSON 2

LESSON 2

Use the figure to answer the question. straight line with point A at one end and point B at the other © 2016 StrongMind. Created using GeoGebra. Which notation is used to name the line segment?

AB (with a line over it) lesson 2

Use the following graph to answer the question. Which answer choices correctly describe the rotation that maps figure ABCD to figure A′B′C′D′? Select two that apply.

a 270∘ clockwise rotation about the origin a 90∘ counterclockwise rotation about the origin lesson 6

line segment

a piece of a line consisting of two endpoints and all points on the line between those two points (noun)

converse

a statement formed by exchanging the hypothesis, p, and the conclusion, q, of a conditional statement and denoted as q⇒p (noun)

line

a straight path that continues forever in two directions and has no width or depth (noun)

ray

a straight path that has a starting point, called an initial point, and continues forever in one direction (noun)

circle

all of the points in a plane that are the same distance from a given point, called the center (noun)

line of symmetry

an imaginary line in a figure in which either side of the line is a mirror image of the other (noun)

center of rotation

the fixed point on a plane about which a figure rotates counterclockwise or clockwise (noun)

diameter

the line segment whose end points are on the circle and midpoint is at the circle's center (noun)

conclusion

the part of a conditional statement that follows the word "then" (noun)

Two coplanar lines that never intersect are called parallel lines. What information, if any, should be changed in the previous sentence to correctly define parallel lines?

The sentence does not need to be changed. checkpoint 1

Use the graph to answer the question. Which statements are true about the transformation that maps triangle ABC to triangle A′B′C′? Select all that apply.

Triangle A′B′C′ is the result of a reflection. The transformation preserves side lengths and angle measures. The transformation is a rigid transformation. lesson 6

A segment is on a number line with endpoints at −13.6 and −6.2. What is the length of the segment?

7.4 lesson 2