- Measure of inscribed angle is^12 of the measure of the arc it intercepts.
- Measure of center angle is 2 (measure of inscribed angle)
- List out the inscribed angle corollaries.
- When working on the multi-step examples, use color to help students to differentiate between which angles
are being worked with and which ones aren’t being worked with. The color will help students to focus on the
appropriate part of the diagram.
IV.AlternativeAssessment
- Walk around and help students as they work.
- Collect student work from the corollaries activity.
- Examine each example and see if it clearly demonstrates or shows the corollary.
- Provide students with feedback/correction in the next class.
Angles of Chords, Secants and Tangents
I.SectionObjectives
- Find the measures of angles formed by chords, secants and tangents.
II.MultipleIntelligences
- In this lesson, you are going to be working with three main theorems. The students need to learn these
theorems and then prove each of the theorems. - Here are some notes to help students to break down each theorem.
- Theorem- the measure of an angle formed by a chord and a tangent that intersects on the circle equals half of
the measure of the intercepted arc. - mangle=^12 marc
- Look at the first diagram and label the chord, tangent, intercepted arc and possible angles to measure.
- Theorem- angles inside a circle
- mangle=^12 (marc1+marc2)
- Theorem- angles outside circle
- mangle=^12 (arc◦ 1 +arc◦ 2 )
- Once the students understand the three theorems, go through the example and proofs in the lesson. Ask the
students to point out where the theorems are illustrated and explained in each. - Discuss each example and proof.
- Allow time for questions.
- Intelligences- linguistic, logical- mathematical, visual- spatial, interpersonal
III.SpecialNeeds/Modifications
- Review chords.
- Review secants.
- Review tangents.
- Review interior angles.
- Review exterior angles.
- Review what an intercepted arc is and how to locate it.
IV.AlternativeAssessment
4.9. Circles