Explain how you can use the inscribed angle theorem to justify its second corollary, that an angle inscribed in a semicircle is a right angle

Answers

Answer 1

Step-by-step explanation:

Explanation:

An inscribed angle is an angle formed by two chords in a circle which have a common endpoint. This common endpoint forms the vertex of the inscribed angle. The other two endpoints define what we call an intercepted arc on the circle. The intercepted arc might be thought of as the part of the circle which is "inside" the inscribed angle. (See the pink part of the circle in the picture above.)

A central angle is any angle whose vertex is located at the center of a circle. A central angle necessarily passes through two points on the circle, which in turn divide the circle into two arcs: a major arc and a minor arc. The minor arc is the smaller of the two arcs, while the major arc is the bigger. We define the arc angle to be the measure of the central angle which intercepts it.

The Inscribed Angle Conjecture I gives the relationship between the measures of an inscribed angle and the intercepted arc angle. It says that the measure of the intercepted arc is twice that of the inscribed angle.

The precise statements of the conjectures are given below. Each conjecture has a linked Sketch Pad demonstration to illustrate its truth (proof by Geometer's Sketch Pad!). The linked activities sheet also include directions for further "hands on" investigations involving these conjectures, as well as geometric problems which utilize their results.

The precise statement of the conjectures:

Conjecture (Inscribed Angles Conjecture I ): In a circle, the measure of an inscribed angle is half the measure of the central angle with the same intercepted arc..

Corollary (Inscribed Angles Conjecture II ): In a circle, two inscribed angles with the same intercepted arc are congruent.

Proof: The measure of each inscribed angle is exactly half the measure of its intercepted arc. Since they have the same intercepted arc, they have the same measure.

Corollary (Inscribed Angles Conjecture III ): Any angle inscribed in a semi-circle is a right angle.

Proof: The intercepted arc for an angle inscribed in a semi-circle is 180 degrees. Therefore the measure of the angle must be half of 180, or 90 degrees. In other words, the angle is a right angle.


Related Questions

Multiply each equation by a constant that would help to eliminate the y terms. 2x-5y=-21 3x-3y=-18 What are the resulting equations?

Answers

Answer:

6x - 15y = -63

15x -15y = -90

Step-by-step explanation:

We need to multiply the two equations by a constant that will eliminate the y terms.

The two equations are:

2x - 5y = -21

3x - 3y = -18

Let us multiply the first by 3 and the second by 6. The resulting equations will be:

6x - 15y = -63

15x -15y = -90

Note: To solve the system of equations we can simply subtract the first from the second.

NEED ANSWER ASAP. WILL MARK THE BRAINLIEST

Use the function below to find f(2)

f(x)=1/3x4^x

Answers

Answer:32/3

Step-by-step explanation:

1/3(2)4^2

1/3(2)(4^2)

2/3(16)

32/2

Answer:

f(2)=16/3

Step-by-step explanation:

f(2)=1/3 (4^2)

f(2)=1/3(16)

f(2)=16/3

Which transformation does not match blue figure to the red flag

Answers

Answer:

the second one trust me

Step-by-step explanation:

What is the approximate circumference of the circle shown below

Answers

I would help you but there is no values shown below!?

If we’re doing the same homework, I’d say 129 cm? But I don’t know what the question is without a picture. Sorry!

PLEASE HELP! SEE ATTACHMENT
it's algebra graphing

Answers

Answer:

a- g(x)= 4/5 x -3

b- slope is 4/5

c-  vertical intercept is y= -3 when x=0

Step-by-step explanation:

Vertical compression : 4/5 f(x)

shift left you add f(x) +1

shift down you subtract : f(x)-1

the result is g(x) = 4/5 f(x) +1-4

A teacher purchased 1 foot long sub to share amongst a group of 4 students. But decided to eat half of it. After dividing the rest of the sub into equal parts how much of a sub will each student recive?

Answers

Answer:

1/8th

Step-by-step explanation:

Answer:

1/8 of the sub or 1.5 inches

Step-by-step explanation:

One foot=12 inches, but the teacher eats half, so we are left with only six inches. then, divide the six inches with the number of students, which is 4. if you divide 12 and 1.5, you'll see that there are a total of 8 pieces, so one student gets 1 out of the 8

Which expression represents the product of 25 and 9 divided by 52

Answers

Answer:

(25*9)/52

Step-by-step explanation:

Answer:

225/9

Step-by-step explanation:

Product of 25 and 9

------------------------------ = 225/52

             52'

When you are given answer choices, please share them.  Thanks.


Size
Small
Medium
Large
Cost
$2.25
$2.50
$2.75
The table above shows the cost of drinks at
Lydia's Lemonade Stand. If the store make $250
on a certain day and twice as many medium
sized drinks as either small or large sized drinks,
how many large sized drinks did the store sell?
E. 15
F. 20
G. 25
H. 50

Answers

The answer is: E

Hope this helps|

In the diagram below, if
AEB=50°, find the measure of
AED.

Answers

Answer: 130ᴼ

Step-by-step explanation:

BD is a straight line so AEB and AED add to equal 180ᴼ

180 - 50 = 130

Answer:

AED = 130

Step-by-step explanation:

AEB and AED form a straight line so they add to 180 degrees

AEB + AED = 180

50 + AED = 180

Subtract 50 from each side

AED = 180-50

AED = 130

What is the solution to the system of equations graphed below? (0, 4) (1, 3) (3, 1) (4, 0)

Answers

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 lines

it aint the ans but Atleast u can find it

Answer:

(-2, 4) and (4, -3)

Step-by-step explanation:

if it’s the one I think it is, then they intersect at 4 and -3 the other numbers are just background noise tbh bc this was the only choice with 4 and -3

what is the exact volume of the cylinder? enter your answer, in terms of pi, in the box.

Answers

Answer:

Step-by-step explanation:

r = 8 in

h = 5 in

Volume of cylinder = πr²h

                                = π * 8 * 8* 5

                                = 320π in³

Answer:

v=hpir^2

h=5

r=8

v=5pi8^2

v=5pi64

v=320pi cubic inches

Step-by-step explanation:

What is 4.5 x 10 to the power of -6 in standard notation?

Answers

Answer:

0.0000045

Step-by-step explanation:

Answer:

.0000045*10 6 power

Step-by-step explanation:

Move decimal point 6 spaces left *10

60 miles/1 hour * 5380/1 mile * 1 hour/60 min * 1 min/60 seconds

Answers

Answer:

Don't understand this

At 7pm, the temperature outside was -5 degree celsius. What does |-5| represent in this situation?

Answers

The number of degrees between 0 and -5 C

Step-by-step explanation:

Hi! It is not 1-5 is is the absolute value of -5. This would be 5 which is the number of degrees between 0 and -5.

Step-by-step explanation:

|-5| who’s absolute value is 5 is representing temp form 0 to -5

What is Temperature ?

Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius

What is modulus?

The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign. For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5.

According to question

At 7pm, the temperature outside was -5

And |-5| = 5 (which is absolute value)

And represent count of temp from 0 to -5 .

Hence, |-5| who’s absolute value is 5 is representing temp form 0 to -5

To know more about modulus here :

https://brainly.com/question/10737199

# SPJ2

Identify the parts of the expression. Then write a word expression for the numerical or algebraic expression.




Please Help!!!! Due in 30 minutes!​

Answers

Answer:

17.3

Step-by-step explanation:

1.5×6+8.3

=9.0+8.3

=17.3

hope it helps

please help! will give brainliest answer!
find x.
a. 2√3
b. 4√3
c. 8√3
d. 8

Answers

Answer:

d. 8

Step-by-step explanation:

sin(α) = opposite/hypotenuse

sin(30°) = 4/x

x = 4/sin(30°) = 4/(1/2) = 8

Multiply. Your answer should be a monomial in standard form. {(-t^7)(-t^5)}

Answers

Answer:

t^12

Step-by-step explanation:

Because both multiplicands are negative, their product will be positive.  Both multiplicands are to the same base:  t.

Therefore, the product is t^(7 + 5), or t^12.

GIVING BRAINLIEST TO PERSON AHO ANSWERS FIRST!!
match the given areas with the correct figure. all areas have been rounded to the nearest whole number. (zoom in to see answers)

Answers

Please refer to the photograph attached for the answer
Hope you find the answers correct
Sorry you will find it really small please zoom in to see the answer to this question
Sorry for the inconvenience about the small answers

What is the volume of a figure with that is 6 inches wide, 3 inches tall and 4 inches long?

Answers

Answer:

6*3*4 = 24*3 = 72 in^3

Answer:

72 cubic inches

Steps:

6*3*4 = 72

Description:

So its asking what is the volume. We know that we need to multiply. SO we get all the numbers from the question that is 6, 3 and 4. Multiply 6 times 3 times 4. You will get the answer that is 72.

Answer: 72 cubic inches

Please mark brainliest

Hope this helps.

Given that y varies directly with x in the table below, what is the value of y if the value of x is 7?
х
2
4
6
10
60
y
12.
24
36
V
37
42
0 0 0 0
48
54

Answers

Answer:

y = 42

Step-by-step explanation:

Given that y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

To find k use an ordered pair from the table.

Using x = 2 when y = 12, then

12 = 2k ( divide both sides by 2 )

6 = k

y = 6x ← equation of variation

When x = 7, then

y = 6 × 7 = 42

Answer:

42

Step-by-step explanation:

just took the quiz and got it right

What is the vertex of the quadratic function below?
y = 3x2 - 12x+17

Answers

Answer:

D (2, 5)

Step-by-step explanation:

To find the vertex of the quadratic function , we will follow the steps below

(x,y) =  [-b/2a  , f(-b/2a)]

x = -b /2a         y = f(-b/2a)

The standard equation of a quadratic equation is  y =ax² + bx + c

compare the above with the equation given, y = 3x² - 12x + 17

a = 3   b= -12   and c= 17

x = -b/2a

x = -(-12)/2(3)

x = 12/6

x = 2

y = f(-b/2a)

y = f (-b/2a) = f(x) = f (2)

y = f(x) =3x² - 12x + 17

To find f(2) simply mean to substitute x = 2 into the quadratic function above. That is;

f(2) = 3(2)² - 12(2) + 17

f(2) =12-24 + 17

f(2) =5

x = 2   and    y  = 5

(x,y)  = (2, 5)

pls help help me need help!!

Answers

Answer:

50 feet

Step-by-step explanation:

[tex]\mid -20 \mid +\mid 30\mid = \\\\20+30= \\\\50[/tex]

Hope this helps!

Answer:

50

Because you just a

on the -20 is a abouloute number which its going to be a postive number so i add the 20 + 30

HELLO, I NEED HELP ASAP :(
Use the distributive property to write the sum as a product.
(-1)·2+(-1)·ₓ

Answers

Answer:

-1(2+x)

Step-by-step explanation:

in the initial equation the -1 was distributed, this answer creates a product (multiplication). -1(2+x)= -2-x

Answer:

(-1)·2+(-1)·ₓ = -1 (2+x)

Step-by-step explanation:

distributive property: ab +ac = a(b+c)

in this case a=-1, b =2, c =x so

(-1)·2+(-1)·ₓ = -1 (2+x)

In Macy’s, a coat has a regular price of x dollars. During a sale, the price of the coat is discounted by 20%. The expression 0.8x describes the discounted price, in dollars, of the coat. Which expression also describes the discounted price, in dollars, of the coat?

plz help me

Answers

Answer:

(1-20%)x or (1-0.2)x or x-0.2x

Step-by-step explanation:

Question 3
the figure needs solving help

Answers

Answer:

ABC = 60

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles

ACD = B+ A

100 = 40 + B

Subtract 40 from each side

100-40 = 40+B -40

60 = B

ABC = 60

Answer:

60°

Step-by-step explanation:

Why would someone choose to use a graphing calculator to solve a system of linear equations instead of graphing by hand? Explain your reasoning.Why would someone choose to use a graphing calculator to solve a system of linear equations instead of graphing by hand? Explain your reasoning.

Answers

a graphing calculator is just easier to graph the points than having to put every point on a piece of graph paper. the calculator also can tell you a bunch of other things like the domain or range or y intercept or x intercept. it’s just all along easier

We would prefer to use a graphing calculator because it will give a more exact solution, because it is easier to read, and because it is faster to do.

How to find a solution of a system of linear equations?

There are multiple ways, one of them is by graphing the lines and seeing where the lines intersect.

Now, there are two ways of doing this, graphing by hand and using a graphing calculator.

There are cases where graphing by hand is enough, but is more time-consuming than using a graphing calculator. But there are cases where the intersection happens at a point with irrational values, these cases is really hard to find the solution in a graph by hand (as it can have mistakes and you can't zoom in). While if you used a graphing calculator, you could zoom is as much as you want, so you would get a really good estimation for the solution.

If you want to learn more about systems of equations, you can read:

https://brainly.com/question/13729904

Which formula could be used to find the volume of a cube with side length equal to s?
s cubed
(6) (s squared)
s squared
(6) (s cubed)

QUESTION 4

Answers

Answer:

s cubed

Step-by-step explanation:

bc volume is length times width times height so it would be s times s times s which is s cubed

Answer: the awnser is a the guy on top or bottem is corect!!!!!!!!!!!!!!!

Step-by-step explanation:

STAY SAFE OUT THERE PLEASE

which inequality is represented by this graph? (0,1) (3,0)

Answers

Answer:

y ≤ -1/3x +1

Step-by-step explanation:

We have a solid line so the inequality has an equals sign.

The graph is shaded underneath so y is less than or equal to

y ≤ -1/3x +1

Answer:

Y<-1/3x+1

Step-by-step explanation:

The line passing through the points is highlighted making it equal to and what makes it less than is that it's shaded on the lower side of the line

I don’t need you to explain just answer.

Answers

Y-intercept:

To find the y-intercept, where the line crosses the y-axis, you need to find the value of y when x is 0.

Slope:

To find the slope of the line, use the equation:

(y₂ - y₁)/(x₂ - x₁)

where (x₁, y₁) is one point on the line and (x₂, y₂) is a different point on the line.

Equation:

y = (y-intercept) + x(slope)

(23+8x-x²)+(x³+x²+34-18x)

Answers

Answer:

x^3 -10x + 57

Step-by-step explanation:

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