Inscribed angle theorem proof (article) | Khan Academy (2024)

Proving that an inscribed angle is half of a central angle that subtends the same arc.

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  • Pranav

    5 years agoPosted 5 years ago. Direct link to Pranav's post “I need help in the proofs...”

    I need help in the proofs for Case 3 in inscribed angles

    (16 votes)

  • toma.gevorkyan8

    7 years agoPosted 7 years ago. Direct link to toma.gevorkyan8's post “Hi Sal, I have a question...”

    Hi Sal, I have a question about the angle theorem proof and I am curious what happened if in all cases there was a radius and the angle defined would I be able to find the arch length by using the angle proof? Or I had to identify the type of angle that I am given to figure out my arch length? Thanks....

    (8 votes)

    • gavinjanz24

      2 years agoPosted 2 years ago. Direct link to gavinjanz24's post “5 years later... I wonder...”

      Inscribed angle theorem proof (article) | Khan Academy (6)

      5 years later... I wonder if Sal is still working on it.

      (14 votes)

  • kjohnson8937

    2 years agoPosted 2 years ago. Direct link to kjohnson8937's post “can I use ψ as a variable...”

    can I use ψ as a variable to measure any angle I want to?

    (4 votes)

    • kubleeka

      2 years agoPosted 2 years ago. Direct link to kubleeka's post “Yes, and it doesn't have ...”

      Yes, and it doesn't have to be an angle. You can assign any variable you like to any symbol you like. You can use Latin letters, Greek letters, Hebrew letters, random shapes, emoji, or anything else.

      It's common practice to use the variables θ, φ, ψ for angle measures (I myself like to use η, since it's the letter before θ), but the rules aren't set in stone. Define whatever you like.

      (8 votes)

  • pandabuff2016

    a year agoPosted a year ago. Direct link to pandabuff2016's post “is it possible to prove c...”

    is it possible to prove case c without proving a & b first?

    (5 votes)

    • jonhlhn.surf

      a year agoPosted a year ago. Direct link to jonhlhn.surf's post “You do not need to prove ...”

      You do not need to prove case B to prove case C, or vice-verse. But in proving case C (or proving case B), you need to prove case A first/along the way.

      (4 votes)

  • Jason Showalter

    4 years agoPosted 4 years ago. Direct link to Jason Showalter's post “What is the greatest meas...”

    What is the greatest measure possible of an inscribed angle of a circle?

    (4 votes)

    • Pat Florence

      4 years agoPosted 4 years ago. Direct link to Pat Florence's post “If the angle were 180, th...”

      If the angle were 180, then it would be a straight angle and the sides would form a tangent line. Anything smaller would make one side of the angle pass through a second point on the circle. So the restriction on the inscribed angle would be:
      0 < ψ < 180

      (5 votes)

  • Akira

    4 years agoPosted 4 years ago. Direct link to Akira's post “What happens to the measu...”

    What happens to the measure of the inscribed angle when its vertex is on the arc? Will it be covered in the future lecture?

    (5 votes)

    • Reynard Seow

      3 years agoPosted 3 years ago. Direct link to Reynard Seow's post “If the vertex of the insc...”

      If the vertex of the inscribed angle is on the arc, then it would be the reflex of the center angle that is 2 times of the inscribed angle. You can probably prove this by slicing the circle in half through the center of the circle and the vertex of the inscribed angle then use Thales' Theorem to reach case A again (kind of a modified version of case B actually).

      (2 votes)

  • taylor k.

    4 years agoPosted 4 years ago. Direct link to taylor k.'s post “Do all questions have the...”

    Do all questions have the lines colored? If not, how would you distinguish between the two?

    (4 votes)

    • victoriamathew12345

      3 years agoPosted 3 years ago. Direct link to victoriamathew12345's post “Normally, to distinguish ...”

      Normally, to distinguish between two lines, you would have letters instead.
      E.g: f(x) vs g(x)

      (3 votes)

  • eperez3463

    a year agoPosted a year ago. Direct link to eperez3463's post “how can i solve this”

    how can i solve this

    (4 votes)

  • Konstantin Zaytsev

    4 years agoPosted 4 years ago. Direct link to Konstantin Zaytsev's post “Why do you write m in fro...”

    Why do you write m in front of the angle sign?

    (1 vote)

    • KC

      4 years agoPosted 4 years ago. Direct link to KC's post “m=measure so it would jus...”

      m=measure so it would just be the measure of the angle

      (5 votes)

  • Trinity Kelly

    5 years agoPosted 5 years ago. Direct link to Trinity Kelly's post “Ok so I have a small ques...”

    Ok so I have a small question, I'm doing something called VLA and they gave me two different equations one to find the radius using the circumference, and the other to find the diameter also using the circumference, the equations were. Circumference/p = diameter, and the other was circumference/2p = radius, but i'm confused cause when I used the second one, it would give me a really big number while the first equation gave me a smaller number. Also sorry if this has nothing to do with what you were talking about Sal, I was waiting until I had enough energy to be able to ask my question.

    (1 vote)

    • kubleeka

      5 years agoPosted 5 years ago. Direct link to kubleeka's post “When you compute C/2π, be...”

      When you compute C/2π, be sure that you're dividing by π by putting the denominator in parentheses. If you just enter C/2*π, the calculator will follow order of operations, computing C/2, then multiplying the result by π.

      (5 votes)

Inscribed angle theorem proof (article) | Khan Academy (2024)

FAQs

What is the statement of the inscribed angle theorem? ›

The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle. Therefore, the angle does not change as its vertex is moved to different positions on the circle.

Is an inscribed angle half of a central angle? ›

An inscribed angle is half the measure of a central angle subtended by the same arc. A central angle is twice the measure of an inscribed angle subtended by the same arc. COB since both are subtended by arc(CB).

How to make an inscribed angle? ›

An inscribed angle in a circle is formed by two chords that have a common end point on the circle. This common end point is the vertex of the angle. Here, the circle with center has the inscribed angle ∠ A B C . The other end points than the vertex, and define the intercepted arc A C ⌢ of the circle.

What is the proof of the angle angle theorem? ›

Two triangles ABC and DEF such that BC is parallel to EF and angle C = angle F and AD = BE. It is given that BC is parallel to EF, angle C is equal in measure to angle F, and |AD| = |BE|. Then, it is true that B = E, because corresponding angles of parallel lines are congruent.

What is the inscribed angle theorem grade 9? ›

The inscribed angle theorem says that an inscribed angle is half the intercepted arc measure. The central angle that subtends the same arc, however, has the same measure as such arc. Therefore, an inscribed angle is half the measure of the corresponding central angle.

How to know if an angle is an inscribed angle? ›

An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of a circle. This is different than the central angle, whose vertex is at the center of a circle. If you recall, the measure of the central angle is congruent to the measure of the minor arc.

What are the rules for inscribed and central angles? ›

Angles whose vertex is on the circumference are called:Inscribed angles. Subtending the same arc means sharing the same arc. In a circumference, the measure of the central angle that subtends the same arc of any inscribed angle is twice the measure of any inscribed angle that subtends the same arc.

Are central angles and inscribed angles measured the same way? ›

A summary of what we did. We set out to prove that the measure of a central angle is double the measure of an inscribed angle when both angles intercept the same arc.

Do inscribed angles add up to 180? ›

Quadrilaterals inscribed in a circle have the distinctive property that their opposite angles are supplementary, adding up to 180 degrees. This arises from the Inscribed Angle Theorem and the congruence of angles intercepting the same arcs.

Are inscribed angles equal? ›

Theorem 70: The measure of an inscribed angle in a circle equals half the measure of its intercepted arc. The following two theorems directly follow from Theorem 70. Theorem 71: If two inscribed angles of a circle intercept the same arc or arcs of equal measure, then the inscribed angles have equal measure.

Can an inscribed angle be 90 degrees? ›

As Diameter is a line segment passing through the center and it has an angle of 180 degrees so the measure of the intercepted arc will be 180 degrees and then by the inscribed angle theorem that inscribed angle will be 90 degrees. so the inscribed angle would be 180/2 = 90 degree.

How do you prove the angle theorem? ›

To prove this theorem, let's assume a pair of intersecting straight lines that form an angle A between them. Now, we know that any two points on a straight line form an angle of 180 degrees between them. So, for the given pair of lines, the remaining angles on both the straight lines would be 180 - A.

How do you prove the inscribed quadrilateral theorem? ›

Proof: In the quadrilateral ABCD can be inscribed in a circle, then we have seen above using the inscribed angle theorem that the sum of either pair of opposite angles = (1/2(a1 + a2 + a3 + a4) = (1/2)360 = 180. Conversely, if the quadrilateral cannot be inscribed, this means that D is not on the circumcircle of ABC.

How do you prove the angle angle side theorem? ›

In angle-angle side(AAS) if two angles and the one non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent.

How do you prove the corresponding angle theorem? ›

Proof of Basic Theorem of Corresponding Angles. Corresponding Angles: Suppose that L, M and T are distinct lines. Then L and M are parallel if and only if corresponding angles of the intersection of L and T, and M and T are equal.

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