slide1 n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Warm-up PowerPoint Presentation
Download Presentation
Warm-up

Loading in 2 Seconds...

play fullscreen
1 / 38

Warm-up - PowerPoint PPT Presentation


  • 128 Views
  • Uploaded on

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

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Warm-up' - decima


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
warm up
Warm-up
  • 1) Solve for x, y, and z.
  • 2) Solve for x.
  • 3) Solve for x.
today s agenda
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
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
Missing Quizzes/Tests 5th
  • 12 Quiz
    • Josi, Conner P, Nikol
  • 10 Test
    • Josi, Andrew, Nikol
  • 10 Test
    • Shelby
  • Check Skyward
missing quizzes tests 6th
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
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
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
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
Theorem 12.3
  • 2 segments tangent to a circle from a point outside the circle are congruent.
theorem 12 4
Theorem 12.4
  • Within a circle or in congruent circles…
    • congruent central angles have congruent chords
    • Angle DOB Angle COA
    • DB CA
theorem 12 41
Theorem 12.4
  • Within a circle or in congruent circles…
    • congruent chords have congruent arcs
    • DB CA
    • Arc DB Arc CA
theorem 12 42
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
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 51
Theorem 12.5
  • Within a circle or in congruent circles…
    • congruent chords are equidistant from the center.
    • XW ZY
    • CL CM
theorem 12 6
Theorem 12.6
  • In a circle, a diameter that is perpendicular to a chord bisects the chord and its arc.
theorem 12 7
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
Theorem 12.8
  • In a circle, the perpendicular bisector of a chord contains the center.
inscribed circle
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
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
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 theorem1
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
Theorem 12.10
  • The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc.
review
Review
  • Identify the Following
    • Chord
    • Diameter
    • Secant Line
secant lines
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
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
Example 2
  • Find the value of x.
theorem 12 11 part 2
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 21
Example 2
  • Find the value of x.
theorem 12 12 part 1
Theorem 12.12 Part 1
  • If two chords intersect, then .
example 3a
Example 3a
  • Find the value of x.
theorem 12 2 part 2
Theorem 12.2 Part 2
  • If 2 secant segments intersect, then (w + x)w = (z + y)y
example 3c
Example 3c
  • Find the value of x.
theorem 12 2 part 3
Theorem 12.2 part 3
  • If a secant segment and a tangent segment intersect, then (y + z)y = t2
example 3b
Example 3b
  • Find the value of z.
assignment
Assignment
  • 12-4 Worksheet
  • Turn in CRT Review
  • Extra Credit
    • pg 707 #1 – 21 all skip 5
  • Check off 12-3