geometry a - unit 1: foundations of geometry lessons 1-5

which of the following statements is biconditional?

a number is an even number if and only if it is divisible by

what notation is used to represent the distance from point a to b?

ab

use the following statement to answer the question. if AB = CD, then AB + 6 = CD+ 6 if the statement is used in a two-column proof, what is the correct reason for the statement?

addition property of equality

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

angle

what term does the statement "the set of all points on a circle between two given points on the circle" define?

arc

the distance between two points on a number line can be found by taking the ____ of the ____ of the coordinates.

blank 1: absolute value blank 2: difference

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

circle

what term does the statement "the set of all points in a plane that are the same distance from a given point" define?

circle

lesson 4

conditional statement

which words or phrases describe parallel lines? select all that apply

coplanar lines never interest

LESSON 2

definitions from undefined terms

unit 1

exam

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.

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.

which statement is correctly written as a conditional statement? if a shape has four sides, then it is a quadrilateral. a shape has four sides when it is a quadrilateral. any four-sided shape is a quadrilateral. a shape has four sides, or it is a quadrilateral.

if a shape has four sides, then it is a quadrilateral

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

which statement is correctly written as a conditional statement?

if four is a perfect square, then you can evaluate its square root.

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.

15. which statement is correctly written as a conditional statement?

if the number 10 is an even number, then it is a composite number.

use the conditional statement to answer the question. if two rays share a common endpoint, then they form an angle. what is the converse of the given conditional statement?

if two rays form an angle, then they share a common endpoint

lesson 5

introduction to proofs

use the figure to answer the question. https://cdstools.flipswitch.com/asset/media/1157936 which term correctly describes the object labeled bb in the figure?

line

which notation is used to name the line segment?

line segment AB (a line on top)

use the following image to answer the question. https://cdstools.flipswitch.com/asset/media/1157799 what statement can be used to prove that vertical angles ∠1 and ∠3 are congruent?

m∠1+ m∠2 = m∠2 + m∠3

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

perpendicular lines

what is the definition of perpendicular lines?

perpendicular lines are two lines that intersect to form four congruent right angles.

use the figure to answer the question. https://cdstools.flipswitch.com/asset/media/1157935 which term correctly describes the object labeled a in the figure?

point

use the image to help you complete this problem.

point: b line: ac plane: p

what must be true in order for two lines to be parallel? select all that apply.

the lines must never intersect the lines must be in the same plane

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.

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

what is the definition of perpendicular lines? two lines that intersect in a way that forms two congruent angles two lines that intersect in a way that forms right angles two lines that intersect in a way that they share more than one common point two lines that intersect in a way that cuts both lines in half

two lines that intersect in a way that forms right angles

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

two-column proof

16. which statement is correctly written as a biconditional statement?

you pass the exam if and only if you score 60% or higher.

the distance between point a and point b is point a = -2 point b = 3

| -2 - 3| = 5

the distance between point a and point b is _[blank]_ units. a = -1 b = 2

|-1 - 2| = 3

use the number line to complete the sentence. x = -4 y = 2 the distance between point x and point y is _[blank]_ units.

|-4 - 2| = 6

a segment is on a number line with endpoints at −5.3 and 8.7 what is the length of the segment?

|-5.3 - 8.7| = 14

a segment is on a number line with endpoints at 2.8 and 4.6. what is the length of the segment?

|2.8 - 4.6| = 1.8

a segment is on a number line with endpoints at -13.6 and -6.2. what is the length of the segment?

7.4

a protractor is used on an angle. one ray of the angle is at 46° and the other day is at 95°. what is the measure of the angle?

95° - 46° = 49°

use the diagram and information to complete the proof. given: ∠1 and ∠2 are supplementary angles.∠2 and ∠3 are supplementary angles. prove:∠1≅∠3 https://cdstools.flipswitch.com/asset/media/1157950 match each reason in the proof with the correct statement.

1. ∠1 and ∠2 are supplementary angles. ∠2 and ∠3 are supplementary angles : given 2. m∠1 + m∠2 = 180, m∠2 + m∠3 = 180 : definition of supplementary angles 3. m∠1 + m∠2 = m∠2 + m∠3 : substitution property of equality 4. m∠1 = m∠3 : subtraction property of equality 5. ∠1 ≅ ∠3 : if two angles have the same measure, then they are congruent.

use the given information to complete the proof. given:∠a and ∠b are supplementary angles. ∠b and ∠c are supplementary angles. prove:∠a≅∠c match the reason with the provided statements to complete the proof.

1. ∠a and ∠b are supplementary angles, ∠b and ∠c are supplementary angles : given 2. m∠a + m∠b = 180, m∠b + m∠c = 180 : definition of supplementary angles 3. m∠a + m∠b = m∠b + m∠c : substitution property of equality 4. m∠a = m∠c : subtraction property of equality 5. ∠a ≅ ∠c : if two angles have the same measure, then hey are congruent.

an angle is measured with a protractor. one ray of the angle is at 37∘ and the other ray is at 112∘. what is the measure of the angle?

112 - 37 = 75

use the following information to answer the question. given: a, b, c, and d are collinear points. b is between a and c. c is between d. b and c are both between a and d. bc = cd prove: ac = bd what is the reason for statement 3?

3. ab + bc = bc + cd : addition property equality

the distance from point a to point is ___ units a = 1 b = 6

5

a protractor is used on an angle. one day of the angle is at 13° and the other rat is at 57°. what is the measure of the angle?

57° - 13° = 44°

use the following image to answer the question. https://cdstools.flipswitch.com/asset/media/1157949 which statement can be used to prove ∠2 ≅∠4?

∠1 is supplementary to both ∠2 and ∠4.

use the following figure to answer the question. what is another name for ∠1?

∠ABC

use the figure to answer the question. what is the correct name for the angle formed by adding ∠1 and ∠2?

∠ABD

use the figure to answer the question. https://cdstools.flipswitch.com/asset/media/1157941 what is another name for ∠2?

∠cbd

use the image to answer the question. which answer choice correctly names the circle?

⊙a

use the figure to answer the question. what is the correct way to name the circle?

⊙b

ue the figure to answer the question. assume that all points on the circle are the same distance from point s. https://cdstools.flipswitch.com/asset/media/1157940 what is the correct name of the circle?

⊙s