Module Seven Review
Please print this study guide prior to participating in the Module Seven Review Session.
Slide Two: [7.01]
Identify and define the following terms below:
Chord:
Diameter:
Concentric circles:
Secant:
Tangent:
Radius:
Two or more circles with congruent radii are called ______.
The distance around a circle is called the ______.
Slide Three: [7.02]
The equation of a circle is written in the form (x-h)^2 + (y-k)^2 = r^2 with center (h, k) and radius r
Write the equation of a circle with a center of (-4,3) and r=6
Write the equation of the circle pictured above.
Slide Four: [7.03]
Formula for Circumference: C=2*pi*r or C=d*pi
Formula for Area: A=pi*r^2
Find the circumference and area of a circle with diameter of 20 inches.
Use pi = 3.14 and round your answers to the hundredth.
What is the diameter of a circle with an area of 25pi cm²?
Slide Five: [7.04]
Postulate 7-1 Arc Addition Postulate - The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.
Theorem 7-1 Congruent Arcs - In the same circle or in two congruent circles, two arcs are congruent if and only if their corresponding central angles are congruent.
Length of arc = (measure of arc/360) * circumference
Name a semicircle
Name a minor arc
Name a major arc
Name a pair of adjacent arcs
What is the measure of arc QP?
What is the measure of arc QR?
What is the measure of arc PQR?
If the diameter of the circle is 20, what is the length of arc QP?
Slide Six: [7.05]
The yellow shaded region is referred to as a ______.
The blue shaded region is referred to as a ______.
The red shaded region is referred to as a(n) ______.
The formula for the area of a sector is
If the red sector of the circle is a semicircle, find the area of the yellow sector with a given radius of 10 units.
Slide Seven [7.06]
Theorem 7-2 Congruent Arcs and Chords - In a circle or congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.
Postulate 7-2 Congruent Chords Congruent Central Angles - If two chords are of equal length, then the central angles are equal.
Theorem 7-3 Perpendicular Diameters and Chords - In a circle, if a diameter is perpendicular to a chord, then it bisects the chord and its arc.
Theorem 7-4 Equidistant Chords are Congruent - In a circle or in congruent circles, if two chords are equidistant from the center of the circle, they are congruent.
Given circle D, if AB = 8 units and AD = 10 units, what is the length of DB?
Given circle O, the midpoint of GH is O. AB = 8x-4 and CD = 4x+24, solve for x, then find AB and CD.
Slide Eight [7.08]
Slide Nine [7.08]
Slide Ten [7.09]
The length of an arc is found using the following formula
Congruent Arcs Theorem – In the same circle or in two congruent circles, two arcs are congruent if and only if their corresponding central angles are congruent.
Theorem 7-5 Inscribed Angle Theorem - the measure of an inscribed angle is one-half the measure of its intercepted arc.
Theorem 7-9 If two secants intersect in the interior of a circle, then the measure of an angle formed is one-half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
Theorem 7-10 If a secant and a tangent intersect at the point of tangency, then the measure of the angle formed is one-half the measure of its intercepted arc.
Theorem 7-11 If two secants, a secant and a tangent, or two tangents intersect in the exterior of a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.
Which theorem best describes how to find the measure of angle one in each example?
Slide Eleven [7.10]
Theorem 7-12 If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.
Theorem 7-13 If a line is perpendicular to a radius of a circle at its endpoint on the circle, then it is a tangent.
Theorem 7-14 If two segments from the same exterior point are tangent to a circle, then they are congruent.
Identify the congruent segments in the figure above.
If LM is tangent to circle K, then what kind of angle is LMK?
Slide Twelve [7.12]
Slide Thirteen [7.12]
Slide Fourteen [7.12]
Slide Fifteen
Use this space to write down any questions you may have so you won’t forget, or you can take notes on here based on the questions asked by your classmates.
Slide Sixteen
Here are some helpful tips!
1. Make sure to read the questions carefully before you select your final answer.
**Are you being asked for x , for an angle or segment?
2. Do NOT use the “<“ key.. Type out the word instead of using the symbol.
3. Make sure to show your work if the problem specifies (essay questions).
4. Make sure when you start the test you have time to complete it. If you close out of it you will be locked out and will NOT be able to access it. Teacher re-set will provide you a new test with different questions.
5. Have Paper, pencil, calculator handy. Be willing to work out your problems on your paper. If needed draw the given figure and label it.