Inscribed Angles and Intercepted Arcs Lesson

Inscribed angles and Intercepted Arcs Lesson

Materials needed: Laminated circles, markers, rulers, protractors

A) 1) Give the students the materials they will need during the lesson

2) Have the students get into groups of two or three

B) 1) Ask the students how many points are on the circle.

2) Have the students draw an equilateral triangle inside of the circle. Ask the students how they know they have drawn an equilateral triangle. Have them label the vertices of the triangle A, B, and C and label the center of the circle as P. Lead the students to since there are 36 dots on the circle so it is 10 degrees between two points.

3) After they draw the triangle define for the students what an inscribed angle and an intercepted arc are. Make an ice cream cone to show which inscribed angle goes with which intercepted arc

4) Have the students find the measures of angles and arcs. Either 360 divided by 3 to get 120, or count using the fact there are 10 degrees between the dots on the circle

5) Ask the students how does the inscribed angle compared to the intercepted arc. Use the freeze option on the ELMO and put the screen up so there can be writing on the board. Make a chart on the board with the number of sides, measure of angle, and measure of the intercepted arc.

6) Listen to see if the students say something about the arc and its angle are supplementary and/or the inscribed angles is one half of the intercepted arc

7) Have students erase their boards C) 1) Do steps 1 – 5 from part B for a square and label the vertices A,B,C, and D 2) Ask the students how they know they have a square 3) Fill in the chart for a square, ask the students if they notice any patterns in the chart. D) 1) Ask the students if they would rather work with a regular pentagon or regular hexagon next. Discuss pros and cons of each E) 1) Do steps 1-5 from part B for a hexagon and label the vertices A,B,C,D,E, and F 2) Listen to see if the students say something about the arc and its angle add up to 360. Find the inscribed angles and intercepted arcs using their protractors and straight edges

F) 1) Ask the students what are some relationships seen in ALL three of the examples. 2) If they do, move on with the lesson. If they don’t then do the same activity with a nonagon. 3) Have students write down the theorem from the screen about the intercepted arc is twice the measure of the inscribed angle into their notes. 4) Erase the board

G) 1) On the circle draw two points on the top half of the circle label them A and B. There should be 100 degrees between points A and B. The students should then draw point C on the bottom half of the circle and place point C in a different location than the other students in their group. 2) Have the students use their rulers to construct inscribed angle ACB and then use their protractor to measure angle ACB 3) Have students bring some examples up to the overhead to show that no matter where point C was drawn the angle ACB was 50 degrees and that minor arc AB was 100 degrees

4) Have the students construct central angle APB and find the measure of central angle APB with a protractor unless they remember what the answer is from a previous day. 5) Have a discussion about the relationship between the central angle ADB and the inscribed angle ACB 6) Write the theorem on the overhead screen into their notes about if two inscribed angles intercept the same arc, then the two angles are congruent 7) Have the students find the measure of major arc ACB. Ask them “How would you do that? “ Make sure to use 3 letters 8) Have the students find the measure of angle ADB. H) 1) Have students draw points A and B anywhere on the circle so that they form a diameter of the circle. Have them explain to a partner how they knew that they drew a diameter 2) Draw point C anywhere on the circle and in a different place compared to other people in their group. Connect points A, B, and C to form a triangle. 3) Have students bring up their drawings to the overhead 4) Ask students “What is the measure of angle ACB?” The measure of angle ACB is 90 and the intercepted arc is 180. 5) Write the theorem about if a right triangle is inscribed inside of a circle then the hypotenuse is a diameter of the circle. Students copy the theorem into their notes. I) (IF TIME) 1) Have the students connect points A, B, C, and D to form a quadrilateral. 2) Have students come up with conjectures. See if they come up with the opposite angles are supplementary. If they do not then help lead them there 3) Write the theorem about a quadrilateral can be inscribed in a circle iff its opposite angles are supplementary on the board.

J) 1) Have students work on the independent practice on the overhead screen. Have them write their answers on the back of the circle worksheet. K) 1) Students work on and complete their exit tickets.