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Geo 7.1 7.2
- 2. ANNOUNCEMENTS Exam IV (Chapter 7) Thursday 4/16 Teaching Presentations Tuesday 4/21 & Thursday 4/23
- 3. TEACHING PROJECT Hippocrates’ Quadrature of the Lune (440 B.C.) Euclid’s Proof of the Pythagorean Theorem (300 B.C.) Archimedes Determination of Circular Area (225 B.C.) Heron’s Formula for Triangular Area (75 A.D) A Gem from Isaac Newton (1665)
- 4. ANGLE / ARC NOTATION
- 9. CIRCLE BASICS Needs three points to identify
- 10. PROBLEM SOLVING The angle addition postulate still holds for arc measure𝑚 𝑅𝑆 + 𝑚 𝑆𝑇 =180° 𝑚 𝑅𝑆 = 𝑚∠𝑅𝑃𝑆 =65°
- 11. CHALLENGE 1. Construct a segment 𝐴𝐵 of length 2 in. 2. Construct a circular arc 𝐴𝐵 with length of 2in. A B A B
- 12. ARC LENGTH x° A B Arc length is only a “portion” or “fraction” of the entire circle l 𝐴𝐵 = 𝑥 360 2𝜋𝑟
- 14. AREA OF A SECTOR
- 15. AREA OF A SECTOR x° A B Sector area is only a “portion” or “fraction” of the entire circle Areasector= 𝑥 360 𝜋𝑟2
- 17. BISECTING CHORDS
- 18. INTERSECTING CHORDS CONJECTURE 1.Construct Circle P 2.Construct chord AB 3.Construct an intersecting chord CD 4.Mark intersection as pt E 5.Measure each of the four A BC D E
- 20. PROBLEM SOLVING
- 21. THE “HOURGLASS” COROLLARY A BC D E What can be said about ΔACE and ΔBDE?
- 22. INSCRIBED ANGLES
- 23. INSCRIBED ANGLES CONJECTURE 1.Construct Circle P 2.Construct inscribed angle ∠RST 3.Construct central angle ∠RPT 4.Find m∠RST 5.Find m∠RPT 6.Conjecture?
- 24. INSCRIBED ANGLES
- 25. THE “STAR TREK” LEMMA
- 26. PROOF! Conjecture: m∠RST = 2 m∠RPT
- 28. PROBLEM SOLVING
- 29. PROBLEM SOLVING
- 30. CIRCLE SEGMENT
- 31. CIRCLE SEGMENT Find the area of the segment
- 32. CIRCLE SEGMENT 1. Construct Circle P with radius 2in. 2. Construct central angle of 80° 3. Find the area of the segment produced.
- 33. CLASSWORK / HOMEWORK Page 369 1 – 4, 5 – 30 odd, 39, 43, 48, 57 Page 378 1 – 11 odd, 19 – 22