Decide whether each statement is true or false. If a statement is true, say which of Euclid’s five postulates apply to it, then write the converse and contrapositive statements, and then decide which of these statements are true (it may help to rewrite the statements in “if-then” form). If it is false, give a counterexample or explain why.

a. A triangle can be drawn from any three points that are not on the same line.
b. A square can be drawn from any four points not on the same line.
c. When two lines intersect, the four angles they make add to 360 degrees.
d. There is only one parallel line to any given line.

Answers

Answer 1

Answer:

A) True

B) False

C) True

D) False

Step-by-step explanation:

A. This statement is True.

From euclid's postulates, if there are three straight lines that intersect each other another, and the sum of the interior angles formed between one of the straight lines and the other two straight lines is less than 180°, then it can be said that the other two straight lines will cross each other if they are both further extended on the same side of the figure in which the sum of the angles was less than 180° as we earlier said.

The converse statement is;

If three lines are drawn and two of the lines converge, then it means the third line can be drawn in such a way that the sum of the interior angles between this third line and the other two lines would be less than 180°.

The contrapositive statement is;

If the sum of the interior angles between the first line and the other two lines equals 180°,then it means that the other two lines will not intersect each other.

B. This statement is false.

The reason is because 4 sides of a square are always equal in length. As a result,all the 4 interior angles must be equal to 90°.

c. This statement is True.

From the first answer above, we saw that if there are three straight lines that intersect each other another, the sum of the interior angles formed between one of the straight lines and the other two straight lines is less than 180°.

Therefore, on the opposite side of the intersection, the sum of the adjacent angles would be equal to 180°

Thus;

180° + 180° = 360°

The converse statements is;

If two lines meet at a point then it means that the sum of the angles at that point equals 360°

The contrapositive statements is;

If the two lines do not meet at any point, then the sum of the angles on each straight line is 180°

d. This statement is False.

The reason is because there is not only one parallel line to any given line because a parallel line can be drawn from aso many points not even on the line in question.


Related Questions

Helpppppppppp fasttttttttttttttttttt

Answers

Answer:

first 2 , second 50, third 8

Step-by-step explanation:

I need to bring my math grade up !!! Does anyone know that answer

Answers

Answer:

2/5 of hangar a = hangar b

Step-by-step explanation:

Which is greater 1.56 or 1.29

Answers

Answer:

1.56 is greater than 1.29. (Check after the decimal point, 5 is greater than 2, so 1.56 is greater than 1.29)

Answer:

I believe that 1.56 is grater than 1.29.

hope this helps.

The lateral surface area is _ square centimeters.

Answers

Answer: 24

Step-by-step explanation:

A​ new, simple test has been developed to detect a particular type of cancer. The test must be evaluated before it is put into use. A medical researcher selects a random sample of 1000 adults and finds​ (by other​ means) that ​3% have this type of cancer. Each of the 1000 adults is given the​ test, and it is found that the test indicates cancer in 99​% of those who have it and in ​2% of those who do not. Based on these​ results, what is the probability of a randomly chosen person having cancer given that the test indicates​ cancer? Of a person having cancer given that the test does not indicate​ cancer?

Answers

Watch the picture for an explanation

Find the following bases.
a. 8% of ? = 20
b. 75% of ? = 30
c. 20% of ? = 45
d. 150% of ? = 36

Answers

Answer:

a.. 8% of ? = 20    240

b.75% of ? = 30    40

c. 20% of ? = 45   225

d. 150% of ? = 36  24

The steps of  answer is in attached file

Hope it helps..

Have a great day : )

Triangle ABC has vertices A (6, 1), B (1,7), and C (-3, -2). The translation to create triangle A'B'C' is (x, y) + (x-1, y +2).

Which of the following will be the coordinates of the vertices of triangle A'B'C?

A (5,2), (0, -4), (0,9)
B (5,3), (0, -4), (0,8)
C (5,3), (0,9), (-4,0)
D (5,2), (1, -3), (0,9)​

Answers

Answer:

I think C is the answer

The hanger image below represents a balanced equation. Find the value of n that makes the equation true.

Answers

Answer:

6

Step-by-step explanation:

16=n +10

subtract 10 from both sides and your left with 6=n

The answer is 6, I already this and it’s pretty easy

Use the equation below to find y, if m=6, x=4, and b= 15. y=mx-b​

Answers

Answer:

9

Step-by-step explanation:

Y = MX-B,

therefore Y = (6*4) - 15,

so Y = 24 - 15

Y = 9

Hey guys I need some help; I would really appreciate it :)

Answers

Their answer is correct so you need explanation?

Find the length of side x in simplest radical form with a rational denominator.

Answers

Answer:

x = 2√3

Step-by-step explanation:

x² = √6² + √6²

x² = 6 + 6 = 12

x = √12 = 2√3

A foreign-car dealer with warehouses in New York and Baltimore receives orders from dealers in Philadelphia and Trenton. The dealer would to minimize the shipping cost. The dealer in Philadelphia needs 3 cars and the dealer in Trenton needs 8. The New York warehouse has 5 cars and the Baltimore warehouse has 9. The cost of shipping cars from Baltimore to Philadelphia is $120 per car, from Baltimore to Trenton $90 per car, from New York to Philadelphia $100 per car, and from New York to Trenton $70 per car. Let x be the number of cars shipped from Baltimore to Trenton, and y be the number of cars shipped from Baltimore to Philadelphia. 5. Write the six inequalities associated with this problem.

Answers

Answer:

[tex]x \ge 0[/tex]  

[tex]y \ge 0[/tex]

[tex]x + y \le 9[/tex]

[tex]8 - x \ge 0[/tex]

[tex]3 - y \ge 0[/tex]

[tex](8 - x) + (3 - y) \le 6[/tex]

Step-by-step explanation:

Given

x = Cars from Baltimore to Trenton

y = Cars from Baltimore to Philadelphia

Required

Write out 6 inequalities

First, 0 or more cars must be shipped to both locations

So:

[tex]x \ge 0[/tex]

[tex]y \ge 0[/tex]

Considering the warehouse in Baltimore.

(1) The warehouse can not ship more than the number of car it has (9).

So:

[tex]x + y \le 9[/tex]

Considering the warehouse in New York.

(1) After shipping cars to Trenton and Philadelphia, the warehouse will have 0 or more cars.

So:

[tex]8 - x \ge 0[/tex] --- To Trenton

[tex]3 - y \ge 0[/tex] --- To Philadelphia

(2) The warehouse cannot send out more than 6.

So:

[tex](8 - x) + (3 - y) \le 6[/tex]

So, the inequalities are:

[tex]x \ge 0[/tex]

[tex]y \ge 0[/tex]

[tex]x + y \le 9[/tex]

[tex]8 - x \ge 0[/tex]

[tex]3 - y \ge 0[/tex]

[tex](8 - x) + (3 - y) \le 6[/tex]

I need halp with one is it?

Answers

Answer: 66ft

Step-by-step explanation:

9 x 5 = 45 + 7 x 3 = 21

45+21=66

Answer:

I am pretty sure it is 66 ft

Step-by-step explanation:

If u just do the top 2x3= 6 and then u multiply 5x12=60 then you add 6 and 60 which is 66

State if the triangles in each pair of similar. If so, state how you know they are similar and complete the similarity statement.


triangle UTS~ ____

a. similar, AA, UED
b. similar, SSS, UDE
c. similar, SAS, UDE
d. not similar​

Answers

Answer:

triangle UTS~∆UED by AAA axiom

ANSWER BOTH QUESTIONS

Answers

Answer:

a and c

Step-by-step explanation:

The opposite of 1.5 is ? So the opposite 1.5 ? Which is equal to the opposite of ? Which is ? The second statement is ?

Answers

I think the opposite of 1.5 is -1.5

If an arithmetic progression satisfies U4=7 , U8=15 .Find U10​

Answers

Answer:

U10 = 19

Step-by-step explanation:

The sequence is [tex]Ux=(x*2)-1[/tex]

x is the coefficient to U.

So, [tex]U10=(10*2)-1[/tex]

Which means [tex]U10=20-1[/tex]

Which means [tex]U10=19[/tex]

And there is your answer.

Hope this helps. Have a nice day.

please help
85-v=213
solve for v

Answers

Step-by-step explanation:

subtract the whole equation by 85 on both sides to get v by itself on the left side

85-85-v=213-85

-v=128

Now we divide the whole equation by negative 1

-1v/-1=128/-1

v=-128

Hope that helps :)

4 + (7-5)^4 on an iready lesson can someone help ?? the four is a exponet

Answers

20. Let me know if you want a step by step.

Can someone please answer this!!

Answers

The answer to your question is B

PLEASE HELP!!! DUE IN 10 MIN!!!

Answers

Answer:

Option B

Step-by-step explanation:

Surface area of a triangular prism = Area of the triangular sides + Area of the rectangular sides

Area of the triangular sides = 2(Area of the triangular base)

                                              = [tex]2[\frac{1}{2}(\text{Base})(\text{Height})][/tex]

                                              = 10 × 12

                                              = 120 ft²

Area of the rectangular sides = (Perimeter of the triangular side)(Height of the prism)    

= (10 + 13 + 13)(15)

= 36 × 15

= 540 ft²

Surface area of the prism = 120 + 540

                                           = 660 square feet

Option B will be the answer.

a quadratic patterns has a second term equal to 1,a third term equal to -6 and fifth term equal to -14 .hence or otherwise calculate the first term of the pattern​

Answers

Answer:

first term of the pattern​ (T₁) : 10

Step-by-step explanation:

T₁  ;    1 ;    -6 ;   T₄ ;    -14  

1-T₁  ;  -6-1   ; T₄-(-6)  ; -14 -T₄    (First Tₙ-Tₙ₋₁)

-8+T₁  = T₄+13 = -2T₄-20            (2nd Tₙ-Tₙ₋₁ is constant)

T₄+13 = -2T₄-20          3T₄ = -33          T₄ = -11

-8+T₁  = T₄+13         -8 + T₁ = -11 + 13 = 2

T₁ = 10

Alice and Finn roll two number cubes. Which of the following rules will make the game fair?

A) Alice wins if a total of 5 is rolled. Finn wins if a total of 9 is rolled.
B) Alice wins if a total of 7 is rolled. Finn wins if a total of 8 is rolled.
C) Alice wins if a total of 3 is rolled. Finn wins if a total of 10 is rolled.
D) Alice wins if a total of 4 is rolled. Finn wins if a total of 11 is rolled.

Answers

Answer:

Alice wins if a total of 4 is rolled. Finn wins if a total of 11 is rolled.

What is the Y value of solution to the following system? (Substitution)
x=3y+4
3x-5y=8
(This is worth 10 points please help this is due in 15 minutes )

Answers

X=1 and y=-1 because when you substitute the x value of x=3y+4 into the second equation and solve for y you get -1

The area of a wall to be tiled in 1.5 metres by 2.5 metres.
Tiles are 50cm by 50cm
The tiles are £0.99 each.
How much will the tiles cost in pounds

Answers

Answer:

£14.85

Step-by-step explanation:

The total number of tiles needed

= 5 × 3

= 15

∴ The total cost of the tiles

= £0.99 × 15

= £14.85


Which of the following must be true?
The diagram is not to scale

Answers

Answer:

AB<BC

Step-by-step explanation:

Just put that answer hope I helped!!

all that make this true i need help

Answers

Answer:

D and E

Step-by-step explanation:

3(23+18)=123

6(18)=108.  6(19)=114.  6(20)=120.  6(22)=132.  6(24)=144

Help answer this!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

D move 6 units to the left and land on -9

Step-by-step explanation:

The dolphin dove down meaning that it went 6 feet below sea level. that would mean -6. If you move 6 spaces to the left, you would land on -9. Hope this helps

Answer:

D. on the number line, move 6 units to the left. End at -9, the Dolphin was 9 feet below sea level

PLEASE HELP!
Find the area of each figure.
18 square units
9 square units
12 square units
24 square units
MATCH THE NUMBERS TO THE GRAPHS!!!!!

Answers

I do know the first figure is 24 square feet.

To get your answer,

Count the amount of the blocks stacked on top each other to make the length, in this case the first photo would be 3, and the width of the block, which is 8. To get the area, you would multiply the length and width together.

Image Form:

l x w = a

(length x width = area)

I hope this is a clear explanation!

Answer:

first one is 24

second one is 12

third one is 9

fourth one is 18

Step-by-step explanation:

what is 7p = -42 i need help i cant find the answer

Answers

Answer:

p=-6

Step-by-step explanation:

So we need to get p by its self so we have to to divide both sides to get the answer. 7p=-42 so p= -6 because we divided -42/7

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