Can you justify that all sides and all angles are equal in a equilateral triangle?

Answers

Answer 1

The basic definition states that all the sides of an equilateral traingle is always same.

so equilateral traingle have same side and is justified  according to the definition of the equilateral traingle.

Now secondly we have to prove that all angles of an equilateral traingle is same  :

in the traingle PQR shown below PQ,QR,PR is the side of the traingle

we have to prove that ∠QPR = ∠PQR = ∠ PRQ.

As we know that all sides length of equilateral traingle are equal.

so PQ=QR=PR

Statement 1:

Angles opposite to equal sides QR and PR are equal so .

=>   ∠QPR = ∠PQR

Statement 2:

Angles opposite to equal sides PR and PQ are equal so .

 =>   ∠PQR = ∠ PRQ.

combining statement 1 and statement 2.

=>  ∠QPR = ∠PQR = ∠ PRQ and hence all three angles are same [Proved]

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Can You Justify That All Sides And All Angles Are Equal In A Equilateral Triangle?

Related Questions

find the slope of the lines graphed below​

Answers

Answer:

use formula

slope m =(y2-y1)/(x2-x1)

Step-by-step explanation:

for first one

(x1,y1)=(2,1)

(x2,y2)=(0,-3)

now

slope m =(y2-y1)/(x2-x1)=(-3-1)/(0-2)=-4/-2=2

try other thank you hope it helps

Find the measure of the exterior <1.

A. 35°
B. 95°
C. 85
D. 120°

Answers

Answer: the answer is c for me I took the test

Step-by-step explanation:

Took the test

A large tank holds 5 x 10^7 gallons of oil. How much oil can be stored in 27 tanks?
Write your answer in scientific notation.

Answers

Answer:

i dunno do the math

Step-by-step explanation:

8y =120 find the solution to the equation

Answers

Answer:

15

Step-by-step explanation:

Answer:

y=15

Step-by-step explanation:

8y=120/8

y=15

Osvoldo has a goal of getting at least 30, percent of his grams of carbohydrates each day from whole grains. Today, he ate 220 grams of carbohydrates, and 55 grams were from whole grains.

Answers

Answer:

No

He ate only 25% from whole grains

He ate 5% less grams from his goal

Step-by-step explanation:

Osvoldo has a goal of getting at least 30, percent of his grams of carbohydrates each day from whole grains. Today, he ate 220 grams of carbohydrates, and 55 grams were from whole grains.

Did Osvoldo meet his goal? Why? , Osvoldo ate grams of whole grains than his goal.

Percent of whole grains ate = grams of whole grain / total carbohydrates) x 100

(55/220) x 100 = 25%

This is less than his goal of 30% by (30% - 25%) 5%

Answer:

No, Osvoldo 11 grams of whole grains less than his goal.

Step-by-step explanation:

30% x 220

30% = 30/100 = 30 ÷ 100

30 ÷ 100 = 0.3

0.3 x 220 = 66

66 - 51 = 11

I need help on this plz and thank you

Answers

Answer:

c.

Step-by-step explanation:

because probability is normally in fraction or decimal

The circumference of a circle is 46.472 millimeters. What is the circle's radius?

Answers

Answer:

r≈7.4

Step-by-step explanation:

C=2πr

Solving forr

r=C

2π=46.47

2·π≈7.39625

Hope this helps! Happy friday!

What is the reference angle of 255°?​

Answers

Answer:

255 degrees is in quadrant 3. The reference angle in this case is the negative x axis to 255 degrees, which is 255 - 180 = 75 degrees

Step-by-step explanation:

BRAINLY TO WHOEVER CAN HELP- ALSO IF YOU GIVE VIA FILESHARE PLS JUST GIVE ME A VERY BREIF SUMMARY CAUSE I CANT OPEN IT

Answers

Answer:

A':2,4

B'4,4

C'2,4

D'2,1.5

Step-by-step explanation:

Just half all the points so in the case of A the original point is 4,8. Dialating by 1/2 is splitting it in half so the new point would be A' 2,4

M
N
Which statement is true about ZJXM and 2NXP?
O ZJXM and 2NXP are complementary
O ZJXM and XNXP are vertical.
O ZJXM and 2NXP are supplementary
O ZJXM and XNXP are adjacent
i

Answers

Answer:

Im late but i was doing the assignment and got A

Step-by-step explanation:

Option A is correct, ∠JXM  and  ∠NXP  are complementary is the true statement.

What are Angles?

An angle is formed when two straight lines or rays meet at a common endpoint.

There are three angles on this straight line JP which are ∠JXM, ∠NXP and ∠MXN

It is shown that ∠MXN is a right angle i.e. 90°.

Then, sum of angle on this line is 180°.

∠JXM + ∠NXP + ∠MXN = 180°

∠JXM + ∠NXP + 90° = 180°

∠JXM + ∠NXP = 180° — 90°

∠JXM + ∠NXP = 90°

From the definition of complementary angles : Two Angles are said to Complementary if their sum is 90° (a Right Angle).

Then, since ∠JXM + ∠NXP add up to 90°, it shows that ∠JXM and ∠NXP are complementary


Hence,  ∠JXM  and  ∠NXP  are complementary is the true statement.

To learn more on Angles click:

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Chase has been playing a game where he can create towns and help his empire expand. Each town he has allows him to create 1.13 times as
many villagers. The game gave Chase 4 villagers to start with. Help Chase expand his empire by solving for how many villagers he can create
with 17 towns. Then explain to Chase how to create an equation to predict the number of villagers for any number of towns. Show your work
and use complete sentences. (10 points)

Answers

Answer:

about 23 villagers

Step-by-step explanation:

17 x 1.13 =19.21 + 4 =23.21

chase would have to use the equation

(n x 1.13)+4

with n being the number of towns

To complete the square for x2 + 8x = -7
you will need to add what number to both sides?
A. -4
B. 12
C. 64
D. 16

Answers

To complete the square, you would add to both sides (8/2)^2 = (4)^2 = 16. So, the correct answer would be D.

HELP ASAP!!!!!!!!! what is the measure of angle x?

Answers

Step-by-step explanation:

x + 149° = 180° {Being linear pair }

x = 180° - 149°

x = 31°

Hope it will help :)❤

Answer:

180-149 = 31

that's right

The New Horizons satellite is currently travelling at a speed of 35,000 mph (miles per hour). How many miles
can it travel in one day?

Answers

840,000 miles.

You multiply 35,000 and 24 since it's 24 hrs in a day and it gives you 840,000!

what are the values of a, b, and c in the quadratic equation -2x² + 4x - 3 =0?

Answers

Answer:

x=1

Step-by-step explanation:

I believe that's the answer sorry if I'm wrong

Chelsea is covering the outside of an old toy box with decorative paper. The box measures 6 inches by 14 inches by 3 inches.

How many square inches of paper is needed to cover the box?

Answers

Answer:

She will be needing 300 square inches of paper

length=14inches

breadth=3inches

height=6inches

TSA= 2(lb+lh+bh)

=2(14×3+14×6+3×6)

=2(42+84+24)

=2×150

=300 square inches

Answer:

69,420

Step-by-step explanation:

69,420 sq ft of decorative paper

What is equivalent to 9?
A:2^3
B:3^-2
C:2^-3
D:3^2

Answers

D is your answer, it equals 9 :)

Given the exponential decay function
y = 39, 752 * (0.925) ^ t which represents the population of a town after t years, what is the rate of decay written as a percentage?

A. 0.073
B. 0.925
C. 7.5
D. 92.5

Answers

The answer is a I hope this helps your welcome

Dana takes a sheet of paper and cuts from one corner to the opposite corner, making two triangles. If the piece of paper is 8 inches long and 5 inches wide, how long is the diagonal cut that Dana made? If necessary, round to the nearest tenth.

Answers

Answer:

9.4 inches

Step-by-step explanation:

The triangle formed is  aright angled triangle with the right angle between the  length and width of the paper cut hence the diagonal represents the hypotenuse side.

Recall that Pythagoras theorem states that

a^2 + b^2 = c^2 where c is the hypotenuse side and a, b are the opposite and adjacent sides

Hence

8^2 + 5^2 = c^2

c^2 = 64 + 25

= 89

Finding the roots of both sides

c = 9.433981132

To the nearest tenth

c = 9.4 inches

The doctor wrote a prescription for 3,110 milliliters of medicine. How many liters of medicine did she prescribe? (1 liter = 1,000 milliliters)

Answers

Answer:

3.11 liters

Step-by-step explanation:

converting mL to L requires dividing by 1000, or moving the decimal point 3 places to the left

in shop a crunchy peanut butter costs $325 for 250g

in shop b crunchy peanut butter costs $408 for 340g

which shop gives better value for money. explain your answer

Answers

Answer:

shop b

Step-by-step explanation:

We can find for example how much 100 grams of peanut butter cost in each shop using a proportion

shop A 100 : 250 = x : 325

x = (325 * 100) / 250 = $130

shop B  100 : 340 = x : 408

x = (408 * 100)/ 340 = $120

We discovered that shop B is cheaper

One factor of f(x)=5x3-5x2-170x+280is(x+7). What are all the roots of the function? Use the Remainder Theorem.

Answers

Answer:

Roots of the f(x) is -7 , 4 and 2.

Step-by-step explanation:

Give that

5x^3-5x^2-170x+280 is (x+7)

One factor of f(x) = x + 7

So,

One root , x = -7

First we determine All factors of the given f(x).

Now divide f(x) by given factor the results are given below:

f(x) = ( x + 7 ) ( 5x² - 30x + 40 )  

    = ( x + 7 ) ( 5x² - 20x - 10x + 40 )  

    = ( x + 7 ) ( 5x( x - 4 ) - 10( x - 40 ) )  

    = ( x + 7 ) ( x - 4 ) ( 5x - 10 )

Now

Place x = -7 in the given function,

f(-7) = 5(-7)³ + 5(-7)² - 170(-7) + 280 = -1715 + 245 + 1190 + 280 = 0

So, First root is -7

Now, Place x = 4

f(4) = 5(4)³ + 5(4)² - 170(4) + 280 = 320 + 80 - 680 + 280 = 0

So, Second root is 4

ANd, place x = 10/5 = 2

f(2) = 5(2)³ + 5(2)² - 170(2) + 280 = 40 + 20 - 340 + 280 = 0

So, Third root is 2

Therefore, Roots of the f(x) is -7 , 4 and 2.

Midory had 0.0085 pounds of chocolate. What is this equation written in scientific notation?

Answers

Answer in scientific notation: 8.3x10^-3

I need help please help me

Answers

Answer:

1: 11/14 2: 1 5/12 3: 1 1/20 4: 7/10 5: 3/4 6: 1 2/9 7: 1 8: 1/8 9: 3/5 10: 23/24

How does the graph of the function g(x) = 2^x- 3 differ from the graph of f(x) = 2^x?
A. It is moved up 3 unit.
B. It is moved down 3 unit.
c. It is moved right 3 unit
D. It is moved left 3 unit.

Answers

It is move right 3 unit
C is answer

Which of the following describes theoretical probability?

Answers

Hi for the answer is there any backstory or answer key at least?

Answer:

Roll of a Die

Step-by-step explanation:

Simplify the expression. Write your answer as a power.
6^7•6^10 divided by 6^4•6^3

Answers

Answer:

[tex] {6}^{10} [/tex]

Step-by-step explanation:

[tex] \frac{6^7•6^{10}}{6^4•6^3} \\ \\ = \frac{6^7•6^{10}}{ {6}^{4 + 3} } \\ \\ = \frac{ \cancel{6^7}•6^{10}}{ \cancel{6^7}} \\ \\ = {6}^{10} [/tex]

Helppp please i need help!!! I was having trouble

Answers

ANSWER - 65.97


V=πr2h
3=π·32·7
3≈65.97345

what is this value? giving thanks and marking brainliest :)

Answers

Answer:

x = 23 degress

Step-by-step explanation:

(x + 2) + 65 = 90

x + 2 = 25

x = 23 degress

Add fractions with unlike denominators

Answers

Answer:

29/12

Step-by-step explanation:

[tex]\frac{7}{4} +\frac{2}{3}[/tex]

7 * 3 / 4 *3 = 21/12

2 * 4 / 3 * 4 = 8/12

[tex]\frac{21}{12} +\frac{8}{12}= \frac{29}{12}[/tex]

Hope this helps!

Answer:

29/12 or 2 and 5/2 as a mixed number

Step-by-step explanation:

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