Geometry, Teacher\'s Edition

(Axel Boer) #1

  • As you work through each example, have the students work through the example in their seats.

  • When all have finished, ask the students to explain how they solved the problem.

  • Then provide feedback.

  • You can verbally check in with the students by having them raise their hands if they had the same answer. This
    will give you a visual cue of how many students were successful and how many were not.


Segments of Chords, Secants and Tangents


I.SectionObjectives



  • Find the lengths of segments associated with circles.


II.MultipleIntelligences



  • Begin this lesson by having the students draw a circle. Then they need to use previously learned information
    and their text to draw in the following.

  • Tangent

  • Chord

  • Secant

  • Tangent segment

  • Chord segment

  • Secant segment

  • Have them use color to draw in each item.

  • When students are finished, explain that we are going to be using these diagrams to illustrate three different
    theorems.

  • When working through each theorem, give students the measurements for each section of the circle, and then
    have them work to figure things out.

  • Theorem- If two chords intersect, the product of segments of chord1 = product of segments of chord2.

  • Then we create two similar triangles.

  • Similar triangles- ratios

  • Add in measures and solve for the missing segment length.

  • Theorem- If two secants are drawn to a common point,a(a+b) =c(c+d)

  • Thea[U+0080][U+0099]s= 1 stsecant

  • Thec[U+0080][U+0099]s= 2 ndsecant

  • Draw in two triangles inside the circle.

  • Similar triangles- ratios

  • Use formula to find the length of the segment of the secant.

  • Theorem- tangent and secant−a(a+b) =c^2

  • Thea[U+0080][U+0099]s=secant

  • The c = the tangent

  • Use it to find the value of the missing tangent length.

  • Intelligences- linguistic, logical- mathematical, visual- spatial, interpersonal, bodily- kinesthetic, intraper-
    sonal.


III.SpecialNeeds/Modifications



  • Review chords.

  • Review tangents.

  • Review secants.


Chapter 4. Geometry TE - Differentiated Instruction
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