Circle Constructions are the Best!

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SWBAT construct tangent lines and inscribed and circumscribed triangles in circles with a review of relationships of chords and radii in circles.

Big Idea

This lesson challenges students to complete three constructions, the first of which is a contest to see who can construct a line tangent to a circle through a given point.

Do Now, Pair-Share and Intro to Constructions

25 minutes

More Constructions and Practice

35 minutes

Section Narrative:   

After completing the construction for a tangent line, teachers can ask students to read aloud and complete the examples on page 3 of the class notes.  The theorems in this part of the lesson help to finish the topics learned in a previous lesson, and will help students connect ideas about circles, arcs, angles, perpendicular lines, parallel lines and Pythagorean Theorem and Pythagorean triplets. 


We will then return to our last two constructions on circumscribed and inscribed triangles.  Teachers can differentiate this portion in many different ways, here are some options below (the most scaffolded is #1 while the extension is #3):


1)     Keep the steps to solve and pre-read with students, show students the construction video, lead students through a practice construction and then ask students to complete their own inscribed or circumscribed triangle

2)    Watch the video, read over the steps to solve, let students try the first construction with guided help or in partners and then ask students to try the second independently. 

3)    Teachers can remove the steps to solve in class notes and provide blank spots for students to fill in steps while watching the video.  Then teachers can ask students to write their steps to solve on the board and ask students to work in pairs to complete the first construction.  Students can then work independently on the second construction. 


After reviewing these constructions, students will have a third try to practice each construction in the last part of class. 

Exit Ticket and Activity/Homework

10 minutes

To wrap up class, teachers can give students a chance to practice in small groups on the last page of scaffolded notes.  These questions will reinforce the applied concepts learned in class and can be done in small groups or pairs.  If students have access to lap tops or their own devices, this would also be a great time to have students re-watch any construction videos that they are struggling with.


The Exit Ticket asks students to write the steps for creating a tangent line to a circle through a given point.  Before the class is over, teachers could ask for a volunteer to review, in their own words, how to complete this construction.