Chord-Chord Product Theorem- If two chords intersect in the interior of a circle, then the products of the lengths of the
segments of the chords are equal.
segments of the chords are equal.
Statement: According to the Chord-Chord Product theorem, the second part of the segment would be 4 because 8 *5 is 40 and making the second part of the segment 4 will give us the product of 40 for this segment.
I chose this theorem because it allows to figure out incomplete segments within a circle. It is important in situations where you need the length of a chord to complete the problem.
Secant-Secant Product Theorem- If two secants intersect in the exterior of a circle, then the product of the lengths of one
secant segment and its external segment equals the product of the lengths of the other secant segment and its external
segment.
I chose this theorem because it allows to figure out incomplete segments within a circle. It is important in situations where you need the length of a chord to complete the problem.
Secant-Secant Product Theorem- If two secants intersect in the exterior of a circle, then the product of the lengths of one
secant segment and its external segment equals the product of the lengths of the other secant segment and its external
segment.
Statement:According to the secant-secant product theorem, the missing length of the second secant is 19 because the product of the first secants length and the outside portion is 20. The inside portion of the second secant would have to be 19 to equal 20.
I chose this theorem because it allows to figure out incomplete segments within a circle and parts of a segment outside the circle. It is important in situations where you need the length of just a certain portion of a whole segment.
Secant-Tangent Product Theorem- If a secant and a tangent intersect in the exterior of a circle, then the product of the
lengths of the secant segment and its external segment equals the length of the tangent segment squared.
I chose this theorem because it allows to figure out incomplete segments within a circle and parts of a segment outside the circle. It is important in situations where you need the length of just a certain portion of a whole segment.
Secant-Tangent Product Theorem- If a secant and a tangent intersect in the exterior of a circle, then the product of the
lengths of the secant segment and its external segment equals the length of the tangent segment squared.
statement: According to the secant-tangent product theorem the tangent would be 8 because the product of the part and whole of the secant is 64 and 8 squared is 64. Therefore 8 is the length of the tangent.
I chose this theorem because it allows to figure out incomplete segments within a circle and parts or whole length of a segment outside the circle. It is important in situations where you need the length of just a certain portion of a whole segment or when trying to find the length of a tangent.
inscribed Angle Theorem- the measure of an inscribed angle is half the measure of its intercepted arc.
I chose this theorem because it allows to figure out incomplete segments within a circle and parts or whole length of a segment outside the circle. It is important in situations where you need the length of just a certain portion of a whole segment or when trying to find the length of a tangent.
inscribed Angle Theorem- the measure of an inscribed angle is half the measure of its intercepted arc.
Statement: According to the inscribed angles theorem angle ABC is 45 degrees because the intercepted arc is 90 degrees so half of that is 45.
I chose this theorem because I've seen it a lot. When you are put into the situation to find multiple variables you're always going to need this to help you find the value of a variable or find a missing angle measure needed to find a variable.
Cyclic Quadrilateral Theorem-If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.
I chose this theorem because I've seen it a lot. When you are put into the situation to find multiple variables you're always going to need this to help you find the value of a variable or find a missing angle measure needed to find a variable.
Cyclic Quadrilateral Theorem-If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.
Statement: Angle BDC is 60 degrees because of the cyclic quadrilateral theorem. It states opposite sides of a cyclic quadrilateral are supplementary.
I chose this theorem because it is another way of using a different polygon to find angle measures in the circle.
Name N/A-If a tangent and a secant (or chord) intersect on a circle at the point of tangency, then the measure of the angle formed is half the measure of its intercepted arc.
I chose this theorem because it is another way of using a different polygon to find angle measures in the circle.
Name N/A-If a tangent and a secant (or chord) intersect on a circle at the point of tangency, then the measure of the angle formed is half the measure of its intercepted arc.
Statement: Angle ABC is 35 degrees because the theorem states that the measure of the angle formed is half the measure of the intercepted arc.
I chose this theorem because it's another example of the inscribed angle. You use this theorem a lot when trying to find angle measures.
Name N/A-If two secants or chords intersect in the interior of a circle, then the measure of each angle formed is half the sum of the measures of its intercepted arcs.
I chose this theorem because it's another example of the inscribed angle. You use this theorem a lot when trying to find angle measures.
Name N/A-If two secants or chords intersect in the interior of a circle, then the measure of each angle formed is half the sum of the measures of its intercepted arcs.
Statement: According to this theorem x is 90 degrees because the average of the two intercepted arcs are 90 degrees.
I chose this theorem because some people may get confused and say that the angle is always the same measure as the intercepted arc. It is not always the case because the average can leave you with different types of numbers.
Name N/A-If a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then the measure of the angle formed is half the difference of the measures of its intercepted arcs.
I chose this theorem because some people may get confused and say that the angle is always the same measure as the intercepted arc. It is not always the case because the average can leave you with different types of numbers.
Name N/A-If a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then the measure of the angle formed is half the difference of the measures of its intercepted arcs.
Statement: According to this theorem x is 90 degrees because the half of the difference of the two intercepted arcs are 90 degrees.
I chose this theorem because it can help find the measure of an angle in the exterior of the circle.
Pythagorean Theorem-a2+b2=c2
I chose this theorem because it can help find the measure of an angle in the exterior of the circle.
Pythagorean Theorem-a2+b2=c2
Statement:Since the legs of the right triangle are 5 and 12, the hypotenuse would be the square root of the sum of 5 squared and 12 squared. That tells us that the hypotenuse is 13.
I chose this theorem because it is involved in finding missing segment lengths inside and outside circles. Triangles appear often inside circles and are also involved in things like finding the radius or the length of two tangents. That's why this is an important theorem.
I chose this theorem because it is involved in finding missing segment lengths inside and outside circles. Triangles appear often inside circles and are also involved in things like finding the radius or the length of two tangents. That's why this is an important theorem.