- Concentric circles- practice drawing them.
IV.AlternativeAssessment
- Assess this lesson through student drawings.
- If the students can draw and label the parts of the circle, then they have an understanding of it.
- If the students can graph the circles, then they have an understanding of the process.
Tangent Lines
I.SectionObjectives
- Find the relationship between a radius and a tangent to a circle.
- Find the relationship between two tangents draw from the same point.
- Circumscribe a circle.
- Find equations of concentric circles.
II.MultipleIntelligences
- Review tangents of a circle and the point of tangency.
- Tangent to a Circle Theorem- work with this theorem by first having the students complete an exploration.
- Have them begin by drawing a circle, the radius and a tangent line.
- Then ask what they can observe about the relationship between the radius and the tangent line. You want them
to discover the theorem on their own and then you can put a name to it for them. - When working with the Pythagorean Theorem and finding the hypotenuse of the triangle, ask students “How
can we find the length of the hypotenuse?” - Once again, you want the students to come up with the Pythagorean Theorem on their own.
- Show Pythagorean Theorem in Example 1.
- When working with the Tangent Segments from a Common External Point Theorem- begin with an explo-
ration. - Have the students draw it out and then record student observations on the board.
- You want them to discover the theorem on their own.
- Intelligences- linguistic, logical- mathematical, visual- spatial, interpersonal, intrapersonal
III.SpecialNeeds/Modifications
- There is a lot of skills/vocabulary to review in this lesson. Do not assume that the students remember.
- Review radius.
- Define circumscribe.
- Define concentric circles.
- Review what is meant by a contradiction.
- Example 1- rather than beginning by proving this theorem through a contradiction, use the exploration first.
Then go through and show how to use a contradiction. Beginning with the contradiction can confuse many
students. - Review the Pythagorean Theorem.
- Review converse statements.
- Example 5- show students where the hypotenuse is located.
- Review how to rationalize a denominator.
- Review HL congruence.
4.9. Circles