Question

https://static.k12.com/nextgen_media/assets/8080657-NG_GMT_C_02_U02_Quiz_03.png

What is the reason for Statement 4 of the two-column proof?

A. Segment Addition Postulate

B. Segment Congruence Postulate

C. Transitive Property of Congruence

D. Symmetric Property of Equality

Answer 1

@Vocaloid

Answer 2

well we have

AB is congruent to BC
BC is congruent to DE

therefore AB is congruent to DE

this is similar to the property

A = B
B = C
then A = C

which starts w/ a T, remember what it is?

Answer 3

it's C

Answer 4

good

Answer 5

What is the reason for Statement 5 of the two-column proof?


A. Linear Pair Postulate

B. Substitution Property of Equality

C. Angle Addition Postulate

D. Angle Congruence Postulate


Given: ∠JNL and ∠MNK are vertical angles. m∠MNK=90°

Prove: ∠JNL is a right angle.

Answer 6

so in step 4 they say m<MNK= 90
in step 5 they replace m<MNK with m<NJL because they're equal

do you remember what property this is?

Answer 7

D

Answer 8

hm not quite, angle congruence postulate states that two congruent angles have two equal angle measures

since we ~substitute~ m<MNK with m<NJL we can say this is the ~substitution property of equality~

Answer 9

What can be used as a reason in a two-column proof?

Select each correct answer.


A. a property of algebra

B. a counterexample

C. a given

D. a conjecture

Answer 10

any ideas? I believe there are two choices that stand out as possible solutions

Answer 11

a property of algebra
a given.

Answer 12

that's what I think too

Answer 13

as usual the first statement is already given

for statement 2, it is decomposing AC into its components AB + BC

which property states that a segment is the sum of its component segments?

Answer 14

segment addition

Answer 15

good

then for statement 4 they are plugging in "AB + BC" for "AC" and "BC + CD" for BD

remember which property is this? it's similar to one we did before

Answer 16

substititon property

Answer 17

good

so to recap

1 = given
2 = segment addition
3 = substitution

Answer 18

well let's look at statements 1-3

MN is congruent to NL
NL is congruent to JN
therefore MN is congruent to JN

which property is this? starts w/ a T

Answer 19

transitive property

Answer 20

good so statement 3 = transitive property of congruence

statement 4 says "given" so we must use a statement that was originally provided at the top

the only one that works is JN congruent to NK

Answer 21

JN NK

Answer 22

yes

then for statement 5 we apply the transitive property of congruence to the original statements

MN congruent to NL
NL congruent to JN
JN congruent to MK

to get MN congruent to MK for statement 5

Answer 23

then there's only one left "definition of isosceles" which makes sense because statement 6 takes MN congruent to NK as two sides of the triangle

Answer 24

so to recap:

3 = transitive
4 = JN congr. NK
5 = MN cong. NK
6 = definition of isosceles

Answer 25

https://static.k12.com/nextgen_media/assets/8078769-NG_GMT_SemA_02_UT_02.png

Kathryn draws three pairs of intersecting lines. In each figure, she measures a pair of angles.

What is a reasonable conjecture for Kathryn to make by recognizing a pattern and using inductive reasoning?


A. When a pair of lines intersect, all of the angles formed are congruent.

B. When a pair of lines intersect, the vertical angles are congruent.

C. When a pair of lines intersect, the vertical angles are acute.

D. When a pair of lines intersect, all of the angles formed are right angles.

Answer 26

any ideas? only one of these statements is true based on the drawing

Answer 27

When a pair of lines intersect, the vertical angles are congruent.

Answer 28

good

Answer 29

https://static.k12.com/nextgen_media/assets/8078791-NG_GMT_SemA_02_UT_06.png

Jasmine draws three scalene triangles. In each figure, she measures each of the angles.

What is a reasonable conjecture for Jasmine to make by recognizing a pattern and using inductive reasoning?

A. In a scalene triangle, all of the angles are acute.

B. In a scalene triangle, none of the angles are congruent.

C. In a scalene triangle, one of the angles is obtuse

D. In a scalene triangle, none of the angles are right angles.

Answer 30

any ideas? notice how there are some angles that are acute, some obtuse, some 90, but which statement seems to be true?

Answer 31

The reasonable conjecture for Jasmine to make by recognizing a pattern and using inductive reasoning is In a scalene triangle, none of the angles are congruent.

Answer 32

good

Answer 33

https://static.k12.com/nextgen_media/assets/8078771-NG_GMT_SemA_02_UT_08.png

Chloe draws three parallelograms. In each figure, she measures a pair of angles, as shown.

What is a reasonable conjecture for Chloe to make by recognizing a pattern and using inductive reasoning?


A. In a parallelogram, all angles are congruent

B. In a parallelogram, consecutive angles are supplementary.

C. In a parallelogram, consecutive angles are congruent.

D. In a parallelogram, all angles are supplementary.

Answer 34

any ideas? notice how angles next to each other add up to 180

Answer 35

In a parallelogram, consecutive
angles are supplementary.

Answer 36

good

Answer 37

Which statement is true about this argument?

Premises:
If two lines are parallel, then the lines do not intersect.
Lines m and n do not intersect.

Conclusion:
Lines m and n are parallel.

Which statement is true about the argument?


A. The argument is not valid because the conclusion does not follow from the premises.

B. The argument is valid by the law of syllogism.

C. The argument is valid by the law of detachment.

D. The argument is not valid because the premises are not true.

Answer 38

this argument is in the format

if p then q
p is given

therefore, q

do you remember which one this is? it's either syllogism or detachment

Answer 39

The argument is not valid because the conclusion does not follow from the premises.

Answer 40

oh

now that i think of it, yeah, the order is mixed up so it would have to be A

Answer 41

Which statement is true about this argument?

Premises:
If a triangle is an isosceles triangle, then it has two sides of equal length.
If a triangle has two sides of equal length, then it has two angles of equal measure.

Conclusion:
If a triangle is an isosceles triangle, then it has two angles of equal measure.




A. The argument is not valid because the premises are not true.

B. The argument is valid by the law of detachment.

C. The argument is not valid because the conclusion does not follow from the premises.

D. The argument is valid by the law of syllogism.

Answer 42

any ideas? we have

if p then q
if q then r

therefore if p then r

Answer 43

it is valid through syllogism

Answer 44

good

Answer 45

Which statement is true about this argument?

Premises:
If a parallelogram has a right angle, then it is a rectangle.
Parallelogram PQRS has a right angle.

Conclusion:
Parallelogram PQRS is a rectangle.

A. The argument is not valid because the conclusion does not follow from the premises.

B. The argument is valid by the law of detachment.

C. The argument is valid by the law of syllogism.

D. The argument is not valid because the premises are not true.

Answer 46

The argument is not valid because the premises are not true.

Answer 47

good (i should really pay more attention >>)

Answer 48

ok

so DF is cut in half into two equal segments DE and EF

so what should blank 1 be?

Answer 49

EF

Answer 50

line on top

Answer 51

good

then for blank 2 they state that segments DE and EF are congruent therefore their measurements are also equal (this would be segment congruence postulate)

Answer 52

for blank three they are saying that DF is the sum of its components DE and EF, remember which property this is?

Answer 53

segment addition

Answer 54

good

for blank 4 they are taking DE + EF = DF

and replacing "EF" with "DE"

so DE + DE = DF

making DF the best choice for blank 4

Answer 55

so to recap:

1. EF with the line seg. notation
2. segment congruence
3. segment addition
4. DF

Answer 56

*make sure the last DF has no line on it

Answer 57

any ideas? notice that <ACB and <BCD make up a straight line and are supplementary

Answer 58

definition of supplementary

Answer 59

that's a good guess but "definition of supplementary" comes a little later

since <ACB and <BCD make up a straight line we call them a "linear pair" and since they sum up to 180 this is the ~linear pair postulate~

Answer 60

mike, i answered that question about the two-column proof twice already lol

(gives medal to voca tho because she slaying @ math)

Answer 61

anyway, the next statement uses "<ACB and <BCD supplementary" to conclude that they add up to 180, that's the definition of supplementary

Answer 62

then for "substitution property of equality" they take the value <BCD = 45 degrees and plug that into the expression <ACB + <BCD = 180, so what would be the result of that?

Answer 63

m<ACB + 45 = 180

Answer 64

awesome

so from there they subtract 45 from both sides to get m<ACB = 135, which property would this be?

Answer 65

subtraction property

Answer 66

awesome

so the next statement uses the "definition of obtuse angle"

we just said that <ACB = 135 so naturally, "<ACB is obtuse" must follow

Answer 67

then finally "ACB is an obtuse triangle" must follow from "the definition of an obtuse triangle" since we just said the triangle has an obtuse angle

Answer 68

so to recap:
linear pair postulate
definition of supplementary
m<ACB + 45 = 180
subtraction
<ACB is obtuse
definition of obtuse angle

Answer 69

blank one is stating that <1 and <2 are congruent, therefore their measurements are equal

would this be "definition of complementary" or "angle congruence postulate"?

Answer 70

angle congruence postulate

Answer 71

awesome

so the next statement

<1 + <3 are complementary therefore m<1 + m<2 = 90 must naturally be the definition of complementary

Answer 72

the next blank mentions the "substitution property"

they take m<1 + m<3 = 90

and plug in m<2 for m<1 , what would be the result of that?

Answer 73

<1

Answer 74

hm not quite

m<1 + m<3 = 90

if we "plug in m<2 for m<1" that means replace m<1 with m<2

so m<2 + m<3 = 90

making "m<3" the appropriate response for the blank

Answer 75

if m<2 + m<3 = 90

<2 and <3 must be complementary so <3 would be the last blank

Answer 76

so to recap:
angle congruence
definition of complementary
m<3
<3

Answer 77

uh

does that say "unit test" in the upper left corner?

Answer 78

yes

Answer 79

i've tried myself and i wasn't good at it

Answer 80

It's against our site policy to assist w/ tests. However I believe you can leverage what we've done so far to make a better attempt at it.

Answer 81

the first is definition of parralelogram

the second is definition of supplementary

the third is m<1 + m<3 = 180

and finally is angle congruence

Answer 82

i believe it's right i might be wrong

Answer 83

I'm really not supposed to help with these at all, sorry.