Download Geometry: Circles Name: ____TEACHER COPY CCSS.Math

Geometry: Circles
Name: ____TEACHER COPY ______________
CCSS.Math.Content.HSG.C.A.1-2
Date: ______________________ Period: _____
Prove that all circles are similar.
Identify and describe relationships among inscribed angles, radii, and chords.
Lesson Outline:
Launch (2 minutes - source: http://jokes4us.com/miscellaneousjokes/mathjokes/geometryjokes.html)
Q: What did the triangle say to the circle?
A: Your pointless!
Introduction (5 minutes): First, let's go over some vocabulary words that we will be using:
circle, chord, point, ray, tangent, secant, point of tangency. Draw a large illustration of these on the
board or overhead.
Investigation (23 minutes): Students will be working with partners but on their own paper. Each
student should have an example for each problem on their own paper. While students work in their
groups, the teacher will circulate around the classroom and make clarifications and corrections as
necessary.
Summary (10 minutes): At this point, the teacher brings the class back together and the whole group
discusses the results of their study. Key points that the students should learn include:
Are all the circles similar? If so, prove it.
How many points of tangency does each circle have?
What is the difference between a lines that are secant or tangent to a circle?
Strategies: This lesson incorporates visuals that help English language learners to understand the concepts.
Pictures are included to help ELL students. Also, having students construct circles and points of tangency that
way is very visual and does not require as many language skills.
Assessment: Informal.
Student understanding will be monitored informally while the teacher circulates around the room
and asks students probing questions. Also, students will summarize their findings at the end of class.
Finally, students will complete a homework assignment on their own that will test their independence
with the material. The assessment will help the teacher know if review is necessary before the next
lesson.
Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
All Rights Reserved by NewMathTeacher.Net
Geometry: Circles
Name: ____________________ ______________
CCSS.Math.Content.HSG.C.A.1-2
Date: ______________________ Period: _____
Prove that all circles are similar.
Identify and describe relationships among inscribed angles, radii, and chords.
Lines that Intersect Circles
Exploring Circles and Tangents
A tangent to a circle is a line that is in the same plane as the circle and that intersects it at exactly one point.
1. Using your compass, construct a circle in the box to the right.
2. Use a straightedge to draw a tangent to the circle.
3. Draw a radius to the point where the tangent intersects the circle.
4. Use a protractor to measure the angle formed by the tangent and radius.
What is the angle measure? The angle measure is _____.
5. Draw three more circles of different sizes and repeat Steps 1–4.
Draw the tangent to each circle in a different position.
Circle #1
Circle #2
Circle #3
6. Describe what you observed about all of the angles that you measured.
7. Explain how you can use your observations to make a conjecture about a tangent to a circle and the
radius drawn to the point where the tangent intersects the circle.
8. Are all the circles similar? If so, prove it.
Answer the following.
1. The _____________ of a circle is the set of all points inside the circle.
2. A _____________ is a line that intersects a circle at two points.
3. Look at circle C above. Why is line t not a secant?
Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
All Rights Reserved by NewMathTeacher.Net
Geometry: Circles
Name: ____________________ ______________
CCSS.Math.Content.HSG.C.A.1-2
Date: ______________________ Period: _____
Prove that all circles are similar.
Identify and describe relationships among inscribed angles, radii, and chords.
Use circle P (above right) to identify each line, segment, or point.
4. secant line
_____________
7. chord
_____________
5. point of tangency
_____________
8. point in the exterior of the circle _____________
6. tangent line
_____________
9. point in the interior of the circle _____________
In each box, write a definition and draw a sketch to describe each the tangent circles (you may
use text if needed).
10. Find the length of each radius. Identify the point of tangency & write the equation of the
tangent line at this point.
radius of R: _____
point of tangency: (___, ___)
radius of S: _____
equation of tangent line: y = __
12. Kilimanjaro, the tallest mountain in Africa, is 19,340 ft tall. What is the distance from the
summit of Kilimanjaro to the horizon to the nearest mile?
Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
All Rights Reserved by NewMathTeacher.Net