geometry stuff ya know

which point is located on ray PQ?

point R

given the statement "if a line is horizontal then it has slope equal to zero" what is its contrapositive?

if a line does not have zero slope then it is not a horizontal line

what is m<PHJ?

120

The logical statement __________ represents the inverse of the conditional statement "if you are human then you were born on earth" which statement is the converse? are the converse and the inverse true statements? explain

1: if you are not human then you were not born on earth 2: if you were born on earth then you are human 3: no because there are nonhuman creatures on earth

let N be an integer in the conditional statement below. if the last digit of N is zero then N is divisible by five. the hypothesis is: the conclusion is: the converse is: the contrapositive is:

1: the last digit of N is zero 2: N is divisible by five 3: if N is divisible by five the last digit of N is zero 4: if N is not divisible by five then N does not end in zero

line segment AB measures 18 units what is D, the distance between tick marks on the number line?

2 units

in the diagram what is M<VSR? m<VSR=

80

which is another way to name <UST?

<TSU

ray CE is the angle bisector of <ACD. which statement about the figure must be true?

>ACE ≅ >DCB

which rays are part of line BE?

AB and AE

let N be a whole number and consider the statements below. P:N is a multiple of two Q:N is an even number which of the following is equivalent to ~Q —> ~P?

P —> Q

given the statement "if jack's pet is a pig then jack's pet cannot fly" which statement represents the converse?

Q --> P, where P = jack's pet is a pig and Q = jack's pet cannot fly

given the conditional statement: P --> ~Q choose the logically equivalent statement.

Q --> ~P

given: m<TRV = 60 m<TRS = (4x) prove: x = 30 what is the missing reason in step 3

angle addition postulate

figure JKLM is a rectangle, so m<KJM = 90 and <KJC ≅ <MLC which reason justifies the statement that <KLC is complementary to <KJC

angles that are congruent are complementary to the same angle

which is a counterexample for the conditional statement shown? if the numerator of a fraction is larger than the denominator of the fraction, then the fraction is greater than 1

any fraction with a positive numerator and a negative denominator

the last step in a proof contains the

conclusion

use the given conditional statement to determine the converse and inverse statements. if a line is vertical then it has undefined slope converse: inverse:

converse: if a line has an undefined slope then it is a vertical line inverse: if a line is not vertical then it does not have an undefined slope

what is the missing reason in the proof? given: abc is a right angle, dbc is a straight angle prove: abc ≅ abd

definition of congruent angles

given: P: 3x + 7 = -5 Q: 4x + 12 = -4 which is the contrapositive of P --> Q

if 4x + 12 ≠ -4, then 3x + 7 ≠ -5

given the original statement "if a number is negative the additive inverse is positive" which are true? select 3 options

A: if P = a number is negative and Q = the additive inverse is positive the original statement is P --> Q B: if P = a number is negative and Q = the additive inverse is positive the inverse of the original statement is ~P --> ~Q D: if Q = a number is negative and P = the additive inverse is positive the contrapositive of the original statement is ~P --> ~Q

which are true regarding the statement "a quadrilateral having exactly one pair of parallel opposite sides is a trapezoid"? check all that apply

A: it is a conditional statement that can be written as "if a quadrilateral has exactly one pair of parallel opposite sides, then it is a trapezoid" B: the hypothesis is: a quadrilateral having exaclty one pair of parallel opposite sides E: the conclusion is: it is a trapezoid

read the statement doubling the dimensions of a rectangle increases the area by a factor of 4 if p represents doubling the dimensions of a rectangle and q represents the area increasing by a factor of 4 which are true? select two options

A: p --> q represents the original conditional statement C: q --> p represents the original conditional statement

line JM intersects line GK at point N which statements are true about the figure? select two options

B: <MNL is complementary to <KNL E: <GNM is supplementary to <JNK

which pairs of statements are logically equivalent? select 2 options

B: the original conditional statement and its contrapositive D: the converse and the inverse of the original conditional statement

let P and Q be statements. identify the truth table for Q --> P

B; TTFF, TFTF, TTFT

which figures can be precisely defined by using only undefined terms? select three options

C: circle D: line segment E: parallel lines

in which diagram do angles 1 and 2 form a linear pair?

D

which defines a line segment?

a piece of a line with two endpoints

what is the inverse of the statement? a number that has exactly two distinct factors its prime

if a number does not have exactly two distinct factors then the number is not prime

given: p: angles XYZ and RST are vertical angles q: angles XYZ and RST are congruent which statement is logically equivalent to p --> q?

if angles XYZ and RST are congruent then they are vertical angles

what is the converse of the statement? perpendicular lines have negative reciprocal slopes.

if lines have negative reciprocal slopes, then they are perpendicular

given the statement "if there is a lighting storm then we won't go swimming" which is the contrapositive?

if we go swimming then there will not be a lighting storm

what is the converse of the conditional statement? if x is even then x + 1 is odd

if x + 1 is odd then x is even

Given: P: x - 5 = 10 q: 4x + 1 = 61 which is the inverse of P --> Q

if x - 5 ≠ 10, then 4x + 1 ≠ 61

which undefined geometric term is described as an infinite set of points that has length but not width?

line

the diagram shows several planes, lines, and points which statement is true about line H

line H is the intersection of planes R and T

angles 1 and 2 are supplementary. which equation represents the relationship between their measures?

m<1 + m<2 = 180

when using a counterexample to prove a conditional statement false, which must be true about the counterexample?

the counterexample must satisfy the hypothesis of the conditional statement

if P is the hypothesis of a conditional statement and Q is the conclusion, which is represented by ~P --> ~Q?

the inverse of the original conditional statement

the statement P --> Q represents "if a number is doubled the result is even" which represents the inverse?

~P --> ~Q where P = a number is doubled and q = the result is even

given the conditional statement ~P --> Q which statement is logically equivalent?

~Q --> P

given a conditional statement P --> Q which statement is logically equivalent?

~Q --> ~P

if an original conditional statement is represented by P --> Q which represents the contrapositive?

~Q --> ~P

given P: today is October 6 and Q: today is nina's birthday. match the conditional statement to its symbolic form

~p —> ~q >>>>>> if today is not october 6, then it is not nina's birthday q —> p >>>>> if today is nina's birthday then it is october 6 p —> q >>>>>> if today is october 6 then it is nina's birthday ~q —> ~p >>>>> if it is not nina's birthday then today is not october 6

angles X and Y are supplementary. angle X is 3 times the measure of angle Y. what is the measure of angle X?

135

consider the conditional statement shown. if any two numbers are prime then their product is odd. what number must be one of the two primes for any counterexample to the statement?

2

in the diagram what is the measure of <WRS

25

point G lies between points F and H on FH if the length of FH is 18 units what is the value of X?

3

if FG = 2 units, FI = 7 units and HI = 1 unit what is GH?

4 units

angle PSR measures 99 what is the measure of <PSQ in degrees?

45

angles 1 and 2 are complementary and congruent. what is the measure of angle 1?

45

angle MON is a straight angle and ray OP bisects <MOQ. what is the measure of <MOP?

61

given that EB bisects <CEA which statements must be true? select three options

A: m<CEA = 90 D: <CEF is a straight angle E: <AEF is a right angle

the diagram shows several points and lines. which statements are true based on the diagram? select two options

B: points J, K, and Q are collinear E: there is only one line that can be drawn through points L and P.

planes S and R both intersect plane T. which statements are true based on the diagram? select 3 options

B: the line containing points A and B lies entirely in plane T D: line Z intersects plane S at point C E: planes R and T intersect at line Y

determine the truth value of the given conditional statement. given: if 3 is an even number then 5+3=8.

a false statement implies a true statement, so the conditional statement is false

the converse of a conditional statement is "if the sum of the exterior angles of a figure is 360 then the figure is a polygon." what is the inverse of the original conditional statement?

if a figure is not a polygon then the sum of the exterior angles is not 360

the inverse of a conditional statement is "if a number is negative, then it has a negative cube root." what is the contrapositive of the original conditional statement?

if a number has a negative cube root, then the number is negative

which is a true conclusion based on the venn diagram?

if a number is prime, it may or may not be odd

given: P: student achieves 90 percent on a geometry final Q: student will receive a passing grade in geometry class. which statement is logically equivalent to Q --> P?

if a student did not receive 90 percent on the geometry final then the student did not pass geometry class

use the diagram to determine a true conditional statement. based on the diagram which is a true statement?

if a student is an honor student then he/she may also be a band member

what is the contrapositive of the conditional statement? if two variables are directly proportional then their graph is a linear function

if the graph of two variables is not a linear function, then the two variables are not directly proportional

if an original conditional statement is represented using p --> q which represents the converse?

q --> p

which statement must be true about the diagram?

ray KM is an angle bisector of <NKL

which statement represents a true conclusion based on the venn diagram

some numbers that are multiples of three are also even numbers

which is logically equivalent to the converse of a conditional statement?

the inverse of the original conditional statement

if the statement is rewritten as a conditional statement in if-then form, which best describes the hypothesis? two lines in a plane intersect at a point

two lines intersect at a point

a flowchart proof

uses a visual representation of the logical flow of steps needed to reach a conclusion

given the conditional statement ~P --> Q, which statement is logically equivalent?

~Q --> P