geo 7.1 7.2
Post on 20-Jul-2015
57 Views
Preview:
TRANSCRIPT
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)
PROBLEM SOLVING
The angle addition postulate still holds for arc measure𝑚 𝑅𝑆 +𝑚 𝑆𝑇 =180°
𝑚 𝑅𝑆 = 𝑚∠𝑅𝑃𝑆 =65°
CHALLENGE
1. Construct a segment 𝐴𝐵 of length 2 in.
2. Construct a circular arc 𝐴𝐵 with length of 2in.
A B
A B
AREA OF A SECTOR
x°
A
B
Sector area is only a “portion” or “fraction” of the entire circle
Areasector=𝑥
360𝜋𝑟2
INTERSECTING CHORDS CONJECTURE1.Construct Circle
P2.Construct chord
AB3.Construct an
intersecting chord CD
4.Mark intersection as pt E
5.Measure each of the four segment lengths
A
BC
D
E
INSCRIBED ANGLES CONJECTURE1.Construct Circle P2.Construct inscribed angle ∠RST3.Construct central angle ∠RPT4.Find m∠RST5.Find m∠RPT6.Conjecture?
CIRCLE SEGMENT
1. Construct Circle P with radius 2in.
2. Construct central angle of 80°3. Find the area of the segment
produced.
top related