Prove that the altitude to the base of an isosceles triangle is also the median to the base in complete sentences:

Answers

Answer 1

Explanation:

The altitude to the base of an isosceles triangle meets the base at right angles, dividing the triangle into two right triangles. The hypotenuse of each of these triangles is one of the congruent sides of the isosceles triangle, so the hypotenuses are congruent. The altitude is congruent to itself, so comprises congruent legs of the right triangles.

The right triangles are congruent to each other by the HL congruence theorem. The remaining side of each of the right triangles is part of the base of the original isosceles triangle. Those sides are congruent by CPCTC, so the altitude meets the base at its midpoint. Hence the altitude to the base is a median of the isosceles triangle.

__

Here's the same argument with vertices defined.

Define isosceles triangle ABC such that AB≅AC. Define altitude AD⊥BC. Then ΔADB and ΔADC are right triangles with AB≅AC and AD≅AD. Then ΔADB≅ΔADC by the HL theorem, and DB≅DC by CPCTC. Hence D is the midpoint of BC, and AD is a median.


Related Questions

On the set of axes below, draw the graph of the equation y = -3/4x + 3. Is the point (3, 2) a solution to the equation? Explain your answer based on the graph drawn

Answers

answer: no (3,2) isn’t a solution because the line on the graph doesn’t go through it and if you plug in the ordered pair in the equation it comes out to be untrue.

(3,2) isn’t a solution because it doesn't satisfy the equation also, the line on the graph doesn’t go through it .

How can we find the solution to an equation?

We do same operations on both the sides so that equality of both expressions doesn't get disturbed.

Solving equations generally means finding the values of the variables used in it for which the considered equation is true.

The graph of the equation is given as y = -3/4x + 3.

We have to find if the point (3, 2) a solution to the equation.

So, we will subtitute the point to to satify the equation;

y = -3/4x + 3.

y = -3/4(3) + 3

y = -9 / 4 + 3

y = 3/3 = 1

Thus, (3,2) isn’t a solution because it doesn't satisfy the equation also, the line on the graph doesn’t go through it .

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After school, Carlos helps his mom at her cake shop, Love and Lace Cakes. Today, he is helping her bake a 3-layer wedding cake. Each layer will be 2 1/2 inches tall and shaped like a rectangular prism. The bottom layer will be 12 inches long and 10 inches wide. The middle layer will be 10 inches long and 8 inches wide. The top layer will be 8 inches long and 6 inches wide. What will the total volume of the wedding cake be?

PLZ HURRY WILL MARK BRAINLIEST

Answers

Multiply length time width times height to find volume of each layer then add the volumes together
Height/length/Width
1st layer: 2 1/2 x 12 x 10
2nd layer: 2 1/2 x 10 x 8
3rd layer: 2 1/2 x 8 x 6
And to make the math easier, turn 2 1/2 into 2.5. They still equal the same thing, but this makes it easier to multiply. Hope this helps!

What is equivalent to -3(-2x + 7)

A. 6x - 21
B. -6x -21
C. 6x + 21
D. 13x
E. 15x

Answers

Answer is A 6x - 21 as the -3 makes the -2x positive and 7 into a negative 21
The answer would be A. 6x - 21
You’d multiply-3 and -2x which gets you a positive 6x. Then you’d multiply -3 and 7 which is -21.

Can someone help me with this two because I am very confused

Answers

Answer:

Let the height of the larger box = h

and length and width of the larger box = l and w , repectively

Now , Let find the volume of the larger box

Volume = length * width * height

So Volume of the larger box = l*w*h = lwh

Now the question says

the height of the smaller box is 80% of the height of the larger box

It means

Height of the smaller box = 80% of h = 0.80*h = 0.80h

and the other two dimensions are same so it means length and width of the smaller box = l and w

so, Volume of the smaller box = l*w*0.80h = 0.80lwh

So the Difference in the volume of the two boxes = Volume of larger box - Volume of smaller box

therefore , Difference in the Volume of two boxes = lwh - 0.80 lwh = 0.20lwh

Step-by-step explanation:

lwh=-0.80 lwh=0.80lwh

A person standing on a moving walkway travels 75 feet in 25 seconds. What equation represents this relationship? How many feet will the person travel in 10 seconds?

Answers

I found someone with the same question as you, good luck !
the person is travel 3 feet per second. and they will travel 30 feet in 10 seconds.

what is the equation

Answers

Answer:   -12 - 3 = -15

Explanation:

We start at -12 which goes in the first box.

Moving to the left 3 units means we subtract off 3, so that's why 3 goes in the second box.

The arrow is pointing at -15 as the final destination, which goes in the final third box.

The equation is -12 -3 = -15

Find the arc length of the partial circle.
Either enter an exact answer in terms of π or use 3.14 π and enter your answer as a decimal.

Answers

Answer:

1/2 pi

Step-by-step explanation:

This is 1/4 of a circle

Find the  circumference and multiply by 1/4

1/4 C

1/4 ( 2*pi*r)  where r is the radius

The radius is 1

1/2 pi*1

1/2 pi

Answer:

Step-by-step explanation:

A full circle has a circumference of 2*pi * r

r = 1

so Full Circle = 2 * PI

1/4 Circle = 2*pi / 4 = 1/2 pi

The length of the arc length = 1/2 pi

Just in case you prefer the more numerical answer, 1/2 * 3.14 = 1.57

Ms. Lopez drew parallelogram M with a height of 6 inches and a base of 6 inches, and parallelogram N with a height of 4 inches and a base of 8 inches. Which parallelogram has the greater area, M or N? help plz​

Answers

Answer:

It is the parellogram M

Step-by-step explanation:

In order to find the area of a parellogram we need do base x height so we compare 6x6 and 8x4 thus making 36>32

Answer:

t is the parellogram M

In order to find the area of a parellogram we need do base x height so we compare 6 x 6 and 8 x 4 thus making 36 > 32

Step-by-step explanation:

HELP THIS IS DUE TOMRROW ANYWAYS THE QUESTION IS
find the coordinate of the midpoint of a segment with the given endpoints.
-7 and -3

Answers

This could be wrong because I'm going into the fifth grade but wouldn't it just be (7,-3)?

Answer: -5

Explanation:
The midpoint between -7 and -3 will be the center of the segment, which would be -5.

Perry saved 4 twenty-dollar bills, 2 ten-dollar bills, 3 dimes, and 2 pennies. Before winter break, he bought a new racing video game for $49.86. How much money did Perry have left?

Answers

Answer:

[see answer below]

Step-by-step explanation:

"Perry saved 4 twenty-dollar bills, 2 ten-dollar bills, 3 dimes, and 2 pennies."

4 * 20 = 80

2 * 10 = 20

3 * 0.1 = 0.3

2 * 0.01 = 0.02

80 + 20 + 0.3 + 0.02 = $100.32

100.32 - 49.86 = 50.46

Hope this helps you.

Answer:

$50.46

Step-by-step explanation:

Math problem for high school

Answers

Answer:

50/3

Step-by-step explanation:

area of triangle = 10

area of circle = 10

area of triangle + area of circle = 20

The white sector of the circle has central angle 60°.

Its area is 1/6 the area of the circle.

To find the gray area, you must subtract the white area from the area of the circle and also subtract the white area from the area of the triangle. Two times the white area is 1/3 the area of the circle.

gray area = 20 - (1/3)10

gray area = 20 - 10/3

gray area = 60/3 - 10/3

gray area = 50/3

Answer:

The white sector of the circle = (1/6) (10) = 10/6 = 5/3

So....the grey area = 10 + 10 - 2 (5/3) = 20 - 10/3 = 60/3 - 10/3 = 50 / 3

MARK BRAINLIEST

25. Ava found that 5 cars passed her house in 10 minutes. Which of the following is a unit rate per hour for this situation? A 10 cars per hour 20 cars per hour B) 30 cars per hour D 40 cars per hour​

Answers

Answer:

B. 30 cars per hour

If 5 cars pass her house in 10 minutes then 30 cars will pass her house per hour

hope you got it xx

Answer :
option B 30 cars per hour

Step by step explanation:

Cars passed in 10 minutes = 5.
Cars passed in 60 minutes (one hour) = unknown

Notice how 10/2 = 5?
Same way 60/2 = 30

Hence, cars passed in 1 hour is 30 cars

solve by factoring
x^2 -10 = 9x

Answers

Answer:

(10,0)(-1,0)

Step-by-step explanation:

x^2 - 9x - 10 = 0

(x - 10)(x + 1) = 0

The two solutions are

x - 10 = 0

x = 10

or

x+1 = 0

x = - 1

Answer:

x=10, x=-1

Step-by-step explanation:

Hi there!

We are given this equation:

x²-10=9x

And we want to solve it by factoring

Factoring is easier to do when all of the terms are on the same side, so let's subtract 9x from both sides

x²-9x-10=0

Now we must think of two numbers that add up to -9, but multiply to get -10

Those numbers are -10 and 1

So factor the polynomial using FOIL:

(x-10)(x+1)=0

Now split and solve via the zero product property:

x-10=0

Add 10 to both sides

x=10

x+1=0

Subtract 1 from both sides

x=-1

Hope this helps!

If x is an integer, what is the least possible value for x that satisfies the inequality?

-5x - 12 < 33

A. -10
B. -9
C. -8
D. 9
E. 10

Answers

Answer:

C. -8

Step-by-step explanation:

We have to solve the inequality by isolating x.

-5x - 12 < 33

Add 12 to both sides.

-5x < 45

Divide both sides by -5 (remember to flip the sign when dividing by a negative).

x > -9

The least possible value for x that satisfies this inequality is -8.

The answer is none other than c witch is -9

Write an equation to find the nth term. Then find ₐ₂₄
1, 3, 5, 7,.......

Answers

The equation to find the nth term is:

an = a+(n-1)d

Where a is the first term in the sequence, which is 1 and d is the difference, which in this sequence the next term is found by adding 2 to the previous term, so d = 2 and n is the term you want to find.

The equation is:

an = 1 + (n-1)2

a24 = 1 + (24-1)2 = 1 + 23(2) = 1+46 = 47

It is 47
All u have to do is download an algebra calculator trust me it helps a lot (calculate84) that’s what I use.

hello!! So I’m in 5th grade (middle school in my state :]) and I have a question.

what is 5 x 23 x 2 ? Please help! I didn’t understand anything in the mah lesson today and I’m behind.

if you can help that’d be a help!

also please tell me how the answer was gotten!


5 x 23 x 2

Answers

Answer:230

Step-by-step explanation:

5 x 23= 115

115 x 2= 230

Ok so this is easy let me help u
5 x 23 x 2
To make it easier let’s pick two numbers to begin with and the sum of those two numbers will be multiplied by 23
5 x 2 is the easiest to multiply so 5 x 2 = 10
And then 10 x 23 = 230
This is it I hope you understood and this helped you

Find the value of x in the isosceles triangle shown below.

Answers

Answer:

sqrt of 41, or A

Step-by-step explanation:

You can cut the iscosles triangle into 2 right triangles as shown on the image, and the base of each will be 4, and the height 5.

The hypotenuse on a right triangle is the square root of the base squared added with the height squared, which would be 16+25, or 41. therefore, X is the sqrt of 41

Answer:

A. x = square root of 41

Step-by-step explanation:

Look at the picture below for the info

Answers

Answer:

x = -3/14

Step-by-step explanation:

1/2(2x-1) = -1/7 -4/7

Combine like terms

1/2(2x-1) = -5/7

Multiply each side by 2

2*1/2(2x-1) = -5/7*2

2x-1 = -10/7

Add 1 to each side

2x-1+1 = -10/7 +1

2x = -10/7 +7/7

2x = -3/7

Divide by 2

2x/2 = -3/7 *1/2

x = -3/14

X = -3/14
I just did it on a calculator:)

The table shows the length and width of Florida at its most distant points.

Determine the prime factorization of the length . Use "^" for the exponent and "x" for the multiplication.

Measurement. Distance (mi)

Length. 500

Width. 160

An example of prime factorization is the following:

Find prime factorization of 50.

1st find the factors of 50 until you only have prime numbers.

1x50

2x25=2x5x5

So the prime factorization of 50 is: 2x5^2

Answers

Answer:

5*10^2

Step-by-step explanation:

Length = 500

500= 5 *100

100=10^2

500= 5 *10^2

5*10^2 hope it helps!!

what comparison does the ratio 6 to 21 represent​

Answers

Answer:

3:7

Step-by-step explanation:

hope it help you....

Answer:

2:7

Step-by-step explanation:

You have to find the common denominator and divide both numbers by that for example: 6 and 21 they can both be equally divided by 3 without becoming a fraction or a decimal.(Pls do correct me if i'm wrong don't be scared to)

A person riding in a elevator travels 240 feet in 30 seconds. What equation represents this relationship? How many feet will the person travel in 10 seconds?

A. y=8x; 8 feet
B. y=1/8x; 1.25 feet
C. y=8x; 80 feet
D. y=6x; 60 feet

Answers

The answer to this question is letter C

We can approach this by first finding the rate of feet per second traveled.

240(feet)/30(seconds)= 8 feet per second.

This answer resembles the slope for answer choice C.

To find the distance traveled in 10 seconds we do 10*8= 80 feet.

I hope this helps, please like and brainliest if correct, thank you!

Answer:

The answer to this question is letter C

We can approach this by first finding the rate of feet per second traveled.

240(feet)/30(seconds)= 8 feet per second.

This answer resembles the slope for answer choice C.

To find the distance traveled in 10 seconds we do 10*8= 80 feetStep-by-step explanation:

have a great day and good luck

a - 6 - 6a = 4

find the value of a

Answers

Answer:

-2

Step-by-step explanation:

a - 6 - 6a = 4

a-6a=10

-5a=10

a=10/-5

a=-2

Answer:

a = -2

Step-by-step explanation:

Add like terms:

a - 6 - 6a = 4

-5a - 6 = 4

Solve for a:

-5a = 10

a = -2

So, a = -2

please help me find what equals to x

Answers

the answer would be 2 i believe
10 ? it’s been awhile since i’ve done math but that side is longer than 12 and longer than the side of 5

In triangle JKL, JKL is a right angle, KM and is an altitude. JL=25 and JM=5, find KM

Answers

Answer:

50

Step-by-step explanation:

i have 30 coins. some of them are dimes, and some of them are quarters. in total, i have $4.05. how many of each coin do i have?

Answers

Answer: 23 dimes & 7 quarters

Step-by-step explanation:

Dimes = 10¢ = $0.10Quarters = 25¢ = $0.25Number of dimes = xNumber of quarters = y

You can create two equations:

[tex]\left \{ {{x + y = 30} \atop {0.10x + 0.25y =4.05}} \right.[/tex]

Rearrange x + y = 30:

[tex]y=30-x[/tex]

Substitute it into the x-value of the other equation & solve:

[tex]0.10x + 0.25y =0.10x + 0.25(30-x)=4.05\\0.10x+7.5-0.25x=4.05\\0.10x-0.25x=4.05-7.5\\-0.15x=-3.45\\x=\frac{-3.45}{-0.15} =23[/tex]

With the x-value, substitute it back to the original equation to find y-value:

[tex]y=30-x=30-23=7[/tex]

Therefore, there are 23 dimes & 7 quarters.

There are 23 dimes and 7 quarters.

Given that, the total number of coins=30.

How to convert dimes to dollars?

To convert dimes to dollars we need to multiply the number of dimes by 0.1.

Let the number of dimes be x, and then the number of quarters will be 30-x.

Now, x×0.1+(30-x)×0.25=4.05

⇒-0.15x=-3.45

⇒x=23

30-x=7

Hence, there are 23 dimes and 7 quarters.

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Each floor of a parking garage can hold 90 cars. When all of the floors are full, there are 450 cars in the garage altogether. What fraction of the cars is parked on the ground floor?

Answers

90 cars out of 450

90 / 450 = 1/5

I guess the number of floors is 5

There would be 5 floors

HELPPPPPPPPPP HELPPPPPP

Answers

Answer:

14c decrease Option D

Step-by-step explanation:

The temperature was 8c at 12 am and -7c at 7 pm to find the difference subtract to get 14c.

whats wrong im only in 7th grade

Step-by-step explanation:

Darren fed his dog 3/4 pound of canned food and 1 1/3 pounds of dry food today. How many pounds of food was that in all?

Answers

Answer:

2 1/12 lbs

Step-by-step explanation:

Add the canned and the dry together

3/4 + 1 1/3

Get a common denominator of 12

3/4 *3/3  + 1 1/3 *4/4

9/12 + 1 4/12

1 13/12

1 + 12/12 + 1/12

2 1/12 lbs

Answer:

2 1/12 pounds of food

Step-by-step explanation:

First find the LCM which is 12 and then convert the two fractions into a 12th.

It would be 1 4/12 and 9/12 and then just add.

Can I have Brainliest?

Solve the equation -10(g - 6) = 65.

Answers

Answer:

g = -1/2

Step-by-step explanation:

-10(g - 6) = 65

Distribute

-10g +60 = 65

Subtract 60 from each side

-10g+60-60 = 65-60

-10g = 5

Divide by -10

-10g/-10 = 5/-10

g = -1/2

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{-10(g - 6) = 65}\\\\\rightarrow\large\textsf{-10g + 60 = 65}\\\\\large\text{SUBTRACT 60 to BOTH SIDES}\\\\\large\textsf{-10g + 60 - 60 = 65 - 60}\\\\\large\text{CANCEL out: 60 - 60 because that gives you 0}\\\\\large\text{KEEP: 65 - 60 because that helps you solve for your g-value}\\\\\large\textsf{65 - 60 = \bf 5}\\\\\large\text{DIVIDE -10 to BOTH SIDES}\\\\\mathsf{\dfrac{-10g}{-10}=\dfrac{5}{-10}}\\\\\large\text{CANCEL out:: }\mathsf{\dfrac{-10}{-10}}\large\text{ because that gives you 1}[/tex]

[tex]\large\text{KEEP: }\mathsf{\dfrac{5}{-10}}\large\text{ because that gives you the g-value answer}\\\\\large\textsf{g = }\mathsf{\dfrac{5}{-10}}\\\\\large\textsf{g =}\mathsf{\dfrac{5\div5}{-10\div5}}\\\\\large\textsf{g = }\mathsf{\bf - \dfrac{1}{2}}\\\\\\\\\boxed{\boxed{\large\textsf{Therefore, your answer is: g = }\mathsf{- \bf \dfrac{1}{2}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}\\\\\\\\\\\frak{Amphitrite1040:)}[/tex]

Help me pleaseeeeeee

Answers

Answer:

B

it's a recurring number therefore it's irrational

The answer is B I believe
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