Warm-up

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# Warm-up - PowerPoint PPT Presentation

Warm-up. 1) Solve for x, y, and z. 2) Solve for x. 3) Solve for x. Today’s Agenda. Review of Chapter 12 Theorems 12.4 Secants angle measures segment proportions Next Class Review/Test Check Skyward. Missing Quizzes/Tests 1st. 12 Quiz

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## Warm-up

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Presentation Transcript
Warm-up
• 1) Solve for x, y, and z.
• 2) Solve for x.
• 3) Solve for x.
Today’s Agenda
• Review of Chapter 12 Theorems
• 12.4 Secants
• angle measures
• segment proportions
• Next Class
• Review/Test
• Check Skyward
Missing Quizzes/Tests 1st
• 12 Quiz
• Sharlanae, Courtney, Lillian, Jordan, Bridger, Johnny, Abigail
• 10 Test
• Armin, Pouria, Jordan,
• 10 Quiz
• Armin, Abigail
Missing Quizzes/Tests 5th
• 12 Quiz
• Josi, Conner P, Nikol
• 10 Test
• Josi, Andrew, Nikol
• 10 Test
• Shelby
• Check Skyward
Missing Quizzes/Tests 6th
• Chapter 12 Quiz
• Julian, Tanner C, Connor
• Chapter 10 Test
• Sam, Connor, Hunter
• Chapter 10 Quiz
• Coleman, Tanner R, Kolton
• Check Skyward
Tangent Lines
• A tangent to a circle is a line that intersects a circle at exactly one point.
• The point of intersection is called

the point of tangency.

Theorem 12-1
• If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.
Theorem 12.2
• Converse of 12.1
• If a line is perpendicular to a radius at its endpoint on the circle, then the line is tangent to the circle.
Theorem 12.3
• 2 segments tangent to a circle from a point outside the circle are congruent.
Theorem 12.4
• Within a circle or in congruent circles…
• congruent central angles have congruent chords
• Angle DOB Angle COA
• DB CA
Theorem 12.4
• Within a circle or in congruent circles…
• congruent chords have congruent arcs
• DB CA
• Arc DB Arc CA
Theorem 12.4
• Within a circle or in congruent circles…
• congruent arcs have congruent central angles
• Arc DB Arc CA
• Angle DOB Angle COA
Theorem 12.5
• Within a circle or in congruent circles…
• chords equidistant from the center are congruent
• (side note) measure distance with perpendicular line
• CL CM
• XW ZY
Theorem 12.5
• Within a circle or in congruent circles…
• congruent chords are equidistant from the center.
• XW ZY
• CL CM
Theorem 12.6
• In a circle, a diameter that is perpendicular to a chord bisects the chord and its arc.
Theorem 12.7
• In a circle, a diameter that bisects a chord (that is not the diameter) is perpendicular to the chord.
Theorem 12.8
• In a circle, the perpendicular bisector of a chord contains the center.
Inscribed Circle
• Inscribed Angle
• Angle whose vertex is on a circle and whose sides are chords.
• Intercepted arc
• Arc created by an inscribed angle.
Theorem 12.9-Inscribed Angle Theorem
• The measure of an inscribed angle is half the measure of its intercepted arc.
• ABC = ½AC
Corollaries to the Inscribed Angle Theorem
• 1) Two inscribed angles that share an intercepted arc are congruent.
• 2) An angle inscribed by a semicircle is a right angle.
Corollaries to the Inscribed Angle Theorem
• 3) The opposite angles of a quadrilateral inscribed in a circle are supplementary.
• angle N + angle O = 180˚
• angle P + angle M = 180˚
Theorem 12.10
• The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc.
Review
• Identify the Following
• Chord
• Diameter
• Secant Line
Secant Lines
• A secant line is a line that intersects 2 sides of a circle.
• Is the diameter a secant?
Theorem 12.11 Part 1
• The measure of an angle formed by 2 lines that intersect inside a circle is the average of the 2 arcs.
• angle 1 =
Example 2
• Find the value of x.
Theorem 12.11 Part 2
• The measure of an angle formed by 2 lines that intersect outside a circle is the difference of the arcsdivided by 2.
• x is the bigger angle
Example 2
• Find the value of x.
Theorem 12.12 Part 1
• If two chords intersect, then .
Example 3a
• Find the value of x.
Theorem 12.2 Part 2
• If 2 secant segments intersect, then (w + x)w = (z + y)y
Example 3c
• Find the value of x.
Theorem 12.2 part 3
• If a secant segment and a tangent segment intersect, then (y + z)y = t2
Example 3b
• Find the value of z.
Assignment
• 12-4 Worksheet
• Turn in CRT Review
• Extra Credit
• pg 707 #1 – 21 all skip 5
• Check off 12-3