how many lines of reflectional symmetry does an equilateral triangle have
Answers
Answer:
only 3 lines of symmetry does an equilateral triangle have.
Explanation:
Since a triangle can have 3 or 1 or no lines of symmetry.
In a equilateral triangle:
*All sides are equal
*All angles are equal i.e each of 60 degree.
Symmetry is when there is an exact replica or reflection of a shape or a line.
Line of symmetry: It is an imaginary line that runs through the center of a line or shape creating two perfectly identical halves.
A line of symmetry for a given triangle must go through each vertex as shown in figure;
Therefore, the equilateral with 3 sides equal has 3 lines of symmetry.
An equilateral triangle has [tex]\fbox{\begin\\\ 3\text{lines}\\\end{minispace}}[/tex] of reflection symmetry.
Further explanation:
A triangle is a two dimensional closed figure which is formed when three non-collinear points are joined. There are three sides, three angles and three vertices of a triangle.
On the basis of sides and angles triangles are classified as follows:
1) Scalene triangle: A triangle in which all the sides and the angles have a unique value is called a scalene triangle.
2) Isosceles triangle: A triangle in which any two sides or two angles are equal then the triangle is called an isosceles triangle.
3) Equilateral triangle: A triangle in which all the sides and the angles are equal then the triangle is called an equilateral triangle.
A line of reflection is defined as a line across which the image of a figure or an object is reflected.
The reflected image is of same size as of the original image.
In case of an equilateral triangle if we drop a median from one of the vertex of the triangle to its opposite side then it is observed that the median divides the equilateral triangle into two equal halves.
From figure 1 (attached in the end) it is observed that the median AD of an equilateral trinagle [tex]\triangle \text{ABC}[/tex] divides the triangle into two equal halves.
As per the above statement it is concluded that the median AD is the line of reflection symmetry for the equilateral triangle [tex]\triangle \text{ABC}[/tex].
Now, similarly if we drop a median form the vertex B or C to its opposite side then it is observed that the triangle into two equal halves.
Figure 2 (attached in the end) shows that the median dropped from the vertex B and C divides the triangle into two equal halves.
This implies that the median BD and CD are also the line of reflection symmetry for the equilateral triangle ABC.
So, the total number of lines of reflection symmetry for an equilateral triangle is [tex]3[/tex].
Thus, an equilateral triangle has [tex]3[/tex] lines of reflection symmetry.
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Answer details
Grade: High school
Subject: Mathematics
Chapter: Triangles
Keywords: Triangle, isosceles, scalene, equilateral, angles, vertex, non-collinear, reflection, symmetry, line of reflection, line of symmetry, median, reflected image.
Related Questions
Which linear inequality is represented by the graph?
a.y >2/3 x – 2
b.y < 2/3x + 2
c.y2/3 > 2/.+ 1
d.y<2/3 x – 1
Answers
Your hair is 6 inches long and grows at a rate of 144 millimeters per year. a. Convert 144 millimeters per year to inches per year. Round your answer to the nearest tenth. b. Write an equation that represents the length y (in inches) of your hair after x years. c. How long is your hair after 4 years?
Answers
B) 56.7x + 6
C) 232.8 inches
The rate of hair growth in inches is 5.67 inches per year and in 4 years hair will be 28.68 inches long.
As mentioned in the question,
Your hair is 6 inches long and grows at a rate of 144 millimeters per year. a. Convert 144 millimeters per year to inches per year.
The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
1 inch = 25.4 millimeters,
For, also 1 millimeters = 1 / 25.4 inches,
So,
144 millimeters per year = 144 / 25.4 inches per year
= 5.67 inches per year
Now,
Growth after 4 years,
= 4 × 5.67 + 6
= 28.68
Thus, the rate of hair growth in inches is 5.67 inches per year and in 4 years hair will be 28.68 inches long.
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Find the equation of the ellipsoid passing through the points (±7,0,0),(0,±1,0)(±7,0,0),(0,±1,0) and (0,0,±4)
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A family pass to amusement park cost $54 using the distributive property write an expression that can be used to find the cost in dollars of 8 family
Answers
I hope this helped! :))
ally and barbara, and katherine will share the cost of a vacation rental for a week. aly agrees to pay 30% of the cost. barbara agrees to pay 0.45 of the coat. katherine will pay the remaining balance. if the total rental coast $960, how much will ally, barbara, and katherine each pay towards the week's rent?
Answers
Ally: $288
Barbara: $432
Katherine: $240
Fred Johnson's total insurance premium is $1,200. His employer pays 60% of the total premium. How much does Fred pay? $480 $720 $2,000 $3,000
Answers
Answer: First option is correct.
Step-by-step explanation:
Since we have given that
Amount of Fred Johnson's total insurance premium = $1200
Percentage of total premium his employer pays = 60%
Remaining percentage of total premium he pays is given by
[tex]100\%-60\%=40\%[/tex]
So, amount of insurance premium Fred Johnson pay is given by
[tex]\frac{40}{100}\times 1200\\\\=40\times 12\\\\=\$480[/tex]
Hence, First option is correct.
What kind of graph is this?
Answers
5.6 times what equals to -19.04
Answers
/5.6. /5.6
-3.4 = x
just divide -19.04 by 5.6 and you get -3.4
The given equation can be rearranged as a division problem: -19.04 divided by 5.6. The solution to this is -3.4. Thus, 5.6 times -3.4 equals -19.04.
Explanation:To answer the question, we must find the unknown variable in your given equation, where you are multiplying a number (5.6) by some unknown figure to get -19.04. This type of math problem is a division problem arranged differently. Instead of saying '5.6 times what equals to -19.04', we can rearrange it to say '-19.04 divided by 5.6 equals what'.
To get the answer, simply divide -19.04 by 5.6, which equals -3.4. So 5.6 times -3.4 equals -19.04.
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which expression is represented by the model below?
Answers
Match the pairs of equations that represent concentric circles. Tiles
Answers
1) Two circles are concentric if they have the same center and different radii.
2) The equation of a circle with center xc, yc, and radius r is:
(x - xc)^2 + (y - yc)^2 = r^2.
So, if you have that equation you can inmediately tell the coordinates of the center and the radius of the circle.
3) You can transform the equations given in your picture to the form (x -xc)^2 + (y -yc)^2 = r2 by completing squares.
Example:
Equation: 3x^2 + 3y^2 + 12x - 6y - 21 = 0
rearrange: 3x^2 + 12x + 3y^2 - 6y = 21
extract common factor 3: 3 (x^2 + 4x) + 3(y^2 -2y) = 3*7
=> (x^2 + 4x) + (y^2 - 2y) = 7
complete squares: (x + 2)^2 - 4 + (y - 1)^2 - 1 = 7
=> (x + 2)^2 + (y - 1)^2 = 12 => center = (-2,1), r = √12.
equation: 4x^2 + 4y^2 + 16x - 8y - 308 = 0
rearrange: 4x^2 + 16x + 4y^2 - 8y = 308
common factor 4: 4 (x^2 + 4x) + 4(y^2 -8y) = 4*77
=> (x^2 + 4x) + (y^2 - 2y) = 77
complete squares: (x + 2)^2 - 4 + (y - 1)^2 - 1 = 77
=> (x + 2)^2 + (y - 1)^2 = 82 => center = (-2,1), r = √82
Therefore, you conclude that these two circumferences have the same center and differet r, so they are concentric.
Which equation represents a line that passes through (–9, –3) and has a slope of –6?
Answers
i m here to
help u
I hope u know the point -slope form
,here, the equation will be
y+3= -6x -54
Colin drove 45 minutes to the airport. He arrived 90 minutes before his flight departed, and then he spent 70 minutes in the air. Once he landed, Colin spent 20 minutes gathering his luggage, and then he drove 35 minutes to his hotel. What must be true of any expression that represents the total time that Colin spent traveling from his house to the hotel? The numbers can be added in any order. The number 45 must be the first addend, and 35 must be the last addend. The numbers must be added in the order 45, 90, 70, 20, and 35. The numbers must be added in either the order 45, 90, 70, 20, and 35 or the order 35, 20, 70, 90, and 45.
Answers
Answer:
The numbers must be added in the order 45, 90, 70, 20, and 35.
Step-by-step explanation:
Answer:
The numbers must be added in the order 45, 90, 70, 20, and 35
Step-by-step explanation:
:3
dr. lee went to a bank to get a loan for some new furniture for the waiting area at her clinic. she wanted to borrow $5,000 to be paid back over 3 years. last week the interest rate was 4.25%. but this week theinterest rate went up to 4.50%. how much additional interest will Dr. lee pay because she waited the extra week
Answers
additional interest is 12.5 dollars.
Most evenings after dinner Duarte spends 30 minutes playing chess with his dad. Write an equation for the number of minutes, m, that Duarte spent playing chess with his dad if they played chess together e evenings.
Answers
number of evening playing chess: e
number of minutes = 30 minutes / play * number of evening playing chess
=> m = 30e
Answer: m = 30e
write 129.04 in words
Answers
Write the value of 1710 in standard form
Answers
1710 is already in simplest, standard form.
Sometimes you'll see it written as 1,710, which for some people is easier to read.
Which of the following is the best example of a characteristic of an experiment?
a.Participants should be selected into the treatment group randomly.
b.Participants are rarely aware that they are part of an experiment.
c.Participants are observed without researchers making changes to their behaviors.
d.The results of an experiment are based on a questionnaire given to a random sample of the population.
Answers
One of the basic feature of an experiment is the selection of participants by means of random method. It is very important to select participants randomly in order to avoid experimental bias that may occur as a result of the participants not been an exact representation of the concerned population.
During a catered lunch, an average of 4 cups of tea are poured per minute. The lunch will last 2 hours. How many gallons of tea should the caterer bring if there are 16 cups in one gallon?
Answers
4 X 60 (minutes per hour)
The lunch last 2 hours so if 240 cups is every hour then 480 cups would be for 2 hours.
Now covert 480 cups to gallons. It takes 16 cups to make 1 gallon. We would divide 480/16 = 30 gallons
Answer with sometimes, always, or never true. Give an example/counterexample.
When a point is reflected across the y-axis, the new point has a negative x-coordinate.
Answers
If the original x coordinate is negative, it will become positive. For example, (-5, 5) would become (5,5), which is a positive x. The sign of the x changes when reflected over the y axis.
Final answer:
The statement that a point reflected across the y-axis results in a point with a negative x-coordinate is sometimes true, depending on the original point's location relative to the y-axis.
Explanation:
When a point is reflected across the y-axis, the result depends on the initial position of the point relative to the y-axis. The statement that the new point has a negative x-coordinate is sometimes true. If a point lies to the right of the y-axis (positive x-coordinate), reflecting it across the y-axis will indeed result in a point with a negative x-coordinate. However, if the original point is to the left of the y-axis (already has a negative x-coordinate), reflecting it across the y-axis will give it a positive x-coordinate.
Example
If the original point is (3, 2), reflecting it across the y-axis results in (-3, 2), which supports the statement.
If the original point is (-4, 5), reflecting it across the y-axis yields (4, 5), which contradicts the statement.
Therefore, the correct answer is sometimes true, demonstrating the importance of considering the position of the original point in relation to the y-axis.
Find all the real fourth roots of 256.
4
-8 and 8
8
-4 and 4
Answers
The 4th roots are {4, 4, -4 and -4}.
Check for yourself: Does 4^4= 256? does (-4)^4 = 256?
Amanda used 3/4 cup of sugar to make 2 dozen cookies. How much sugar is in each cookie? (Dozen=12)
Answers
Solve the following equations. Some equations will have a single answer, others will have no solution, and still others will have infinite solutions
1. 2x + 2x + 2 = 4x + 2
2. 3(x − 1) = 2x + 9
3. 2x + 8 = 2(x + 4)
4. 2x − x + 7 = x + 3 + 4
Answers
3(x − 1) = 2x + 9 = x=9
All values of x are solutions
All values of x are solutions
Andreus made $625 mowing yards. He worked for 5 consecutive days and earned the same amount of money each day. How much money did Andreus earn per day
Answers
Enter the degree of the polynomial
5x5 + 8x2 + 2x – 3x9 – 8x4 – 4x5
Answers
The degree of a term is the sum of the exponents of all the variables of the term,. A plain variable has degree 1.
One term is -3x^9.
That has the largest exponent of any term, so the degree is 9.
Answer:
9
Step-by-step explanation:
I got it right on ape-x
What is 600000-347201
Answers
What is the sales tax on a jacket priced at $350 if the sales tax rate is 7%
Answers
Your sale tax for a jacket would be $24.50.
Write these decimal fractions in words 0.17
Answers
One tenth and seven hundredth
Seventeen hundredth
Information about a shipment of mirrors to a local store is shown.
Of all of the medium mirrors that were shipped, how many of them were broken?
A. 68
B. 78
C. 164
D. 208
Answers
480-214-102= 164
From here, subtract the number of mirrors that are not broken.
164-96= 68
Final answer: 68 broken medium mirrors, A
The table is an illustration of a two-way table
The number of medium mirrors that were not broken are 68
Start by calculating the number of medium mirrors
Medium = 480 - 214 - 102
Evaluate the difference
Medium = 164
From the question 96 mirrors are not broken.
So, the number of broken mirror is:
Broken = 164 - 96
Evaluate the difference
Broken = 68
Hence, the number of medium mirrors that were not broken are 68
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The airport garage charges $5 to park for the first hour and then $3.50 an hour for any additional hours. Ben paid $57.50 to park there one day when he flew to another city. How many hours was he parked at the airport?
Answers
Final answer:
Ben was parked at the airport for a total of 16 hours, after calculating the initial cost for the first hour and then dividing the remainder by the hourly rate for additional hours.
Explanation:
The student's question asks how many hours Ben was parked at the airport, given that the parking cost is $5 for the first hour and $3.50 for each additional hour, with a total fee of $57.50.
First, we subtract the initial $5 from the total cost to determine the cost of additional hours:
$57.50 - $5 = $52.50 for additional hours
Next, we divide the remaining cost by the hourly rate for additional hours to find the number of additional hours Ben parked:
$52.50 ÷ $3.50/hour = 15 hours
Finally, we add the first hour to the additional hours to calculate the total hours parked:
15 hours + 1 hour = 16 hours
Thus, Ben was parked at the airport for a total of 16 hours.
Which linear function has the same y-intercept as the one that is represented by the graph?
Answers
on the graph x = 0 , y = 3
function
y = 2x + 3 when x = 0
y = 3
answer
C. y = 2x + 3