Date: 11.3 Notes: Congruent Chords and Arcs Lesson Objective: Recognize and use relationships between arcs, chords and diameters. CCSS: G.C.2, G.MG.3.

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Presentation transcript:

Date: 11.3 Notes: Congruent Chords and Arcs Lesson Objective: Recognize and use relationships between arcs, chords and diameters. CCSS: G.C.2, G.MG.3 You will need: compass, ruler, colored pens Real-World App: How can we tell the slices of pizza are congruent? This is Jeopardy!: This is the exact circumference of a circle with an inscribed rectangle with length 4 and width 2.

Lesson 1: Congruent Chords and Arcs Drop down about 2” and plot P on a blue line about 2” from the margin. Use a compass to draw a 3” circle to model a pizza. Divide your pizza into 8 equal pieces using a compass. P P

Lesson 1: Congruent Chords and Arcs Highlight 2 pieces of pizza that are not adjacent to each other. Label one AB and one CD. What tells you that the pieces are equal in size? P P A B D C

Lesson 1: Congruent Chords and Arcs Why is / APB / CPD? P P A B D C

Lesson 1: Congruent Chords and Arcs Draw chords AB and CD. P P A B D C

Lesson 1: Congruent Chords and Arcs If central / s are, then the corresponding arcs and chords are : / APB / CPD, AB CB, AB CB P P A B D C

Lesson 1: Congruent Chords and Arcs A.

Lesson 1: Congruent Chords and Arcs B.

Lesson 2: More Congruent Chords

Lesson 2: More Congruent Chords

Lesson 3: | Chords and Diameters Construct circle C with 2” diameter. Draw chord XY. Construct AB | XY. Label the intersection of AB and XY point Z. What do you notice about AB? X Y C

Lesson 3: | Chords and Diameters A X Y B C Z

Lesson 3: | Chords and Diameters A.

Lesson 3: | Chords and Diameters B.Find NP.

Lesson 3: | Chords and Diameters C.

11.3: Do I Get It? Yes or No

11.3: Do I Get It? Continued In the stained glass window, diameter GH is 30” long, chord KM is 22” long and arc KM is 85°. Find the following: 4.KL 5.JL 6.mHM