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Lesson Plan #71
Class: Geometry
Date: Friday March 8th, 2013
Topic: Arcs and chords
Aim: What are some relationships between chords and the arcs created by those chords?
Objectives:
1) Students will know some relationships between chords and the arcs created by those chords?
HW # 71:
Page 347 #’s 1-10
Do Now:
̂ ≅ 𝐶𝐷
̂
In circle O, 𝐴𝐵
̅̅̅̅, 𝑂𝐵
̅̅̅̅ , 𝑂𝐶
̅̅̅̅ , and 𝑂𝐷
̅̅̅̅.
Draw radii 𝑂𝐴
How could you show ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐶𝐷?
In circle O, ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐶𝐷
̅̅̅̅
Draw radii 𝑂𝐴, ̅̅̅̅
𝑂𝐵 , ̅̅̅̅
𝑂𝐶 , and ̅̅̅̅
𝑂𝐷 .
̂ ≅ 𝐶𝐷
̂?
How could you show 𝐴𝐵
PROCEDURE:
Write the Aim and Do Now
Get students working!
Take attendance
Give Back HW
Collect HW
Go over the Do Now
Theorem: In the same circle or in congruent circles:
1) Congruent arcs have congruent ___________
2) Congruent chords have congruent ___________
Assignment #1:
In Circle O, diameter ̅̅̅̅
𝐶𝐷 is perpendicular to chord ̅̅̅̅
𝐴𝐵
̅̅̅̅
̅̅̅̅
Draw chords 𝑂𝐴 and 𝑂𝐵 .
How can you prove that ̅̅̅̅
𝐴𝐸 ≅ ̅̅̅̅
𝐵𝐸 ?
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Theorem:
A diameter that is perpendicular to a chord bisects the chord and its arc.
Assignment #2:
Find the value of x and y.
Assignment #3:
Find the value of x
Theorem: In the same circle or in congruent circles,
Chords equally distant from the center are _____________
Congruent chords are equally distant from the ___________
Example #1: Find x and y
̂
Example #2: Find x, y and m𝐴𝐵
Example #3: Find x and y
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Exercise #1:
In the diagram at right of circle O, diameter ̅̅̅̅
𝐴𝐵 is perpendicular to chord ̅̅̅̅
𝐶𝐷 at E.
̅̅̅̅
If AO = 10 and BE = 4, find the length of 𝐶𝐸
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