Corresponding parts of congruent triangles are congruent. (CPCTC)
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1 Corresponding parts of congruent triangles are congruent. (CPCTC)
2 Corresponding parts of congruent triangles are congruent. (CPCTC) Definition: Congruent triangles: Triangles that have all corresponding parts congruent are congruent.
3 C Z B X Y
4 Definition: Circle: circle is the set of all points in a plane the same distance from a given point.
5 Definition: Circle: circle is the set of all points in a plane the same distance from a given point.
6 Definition: Circle: circle is the set of all points in a plane the same distance from a given point.
7 Definition: Circle: circle is the set of all points in a plane the same distance from a given point. Points L, S, and C are points on the circle. L S C
8 Definition: Radius: radius is a segment with one endpoint on a circle and the other endpoint at the center of the circle. L, S and C are all radii of the circle. L S C
9 Definition: Chord: segment that has both endpoints on the same circle is a chord. CL, BS and LS are all chords of the circle. L S C B
10 Definition: Diameter: chord that passes through the center of a circle is a diameter. BS is a diameter of the circle. L S C B
11 The ratio of the circumference to the diameter of all circles is the same.
12 The ratio of the circumference to the diameter of all circles is the same. That ratio is called pi (π).
13 The ratio of the circumference to the diameter of all circles is the same. That ratio is called pi (π). Pi is an irrational number. That means that it is an infinite, nonrepeating decimal. common approximation for pi is 3.14.
14 March 14 (3/14) is often celebrated as "Pi Day."
15 March 14 (3/14) is often celebrated as "Pi Day." The next two digits of pi are 1 and 5 (3.1415), so in 2015 Pi Day will be extra special (3/14/15).
16 March 14 (3/14) is often celebrated as "Pi Day." The next two digits of pi are 1 and 5 (3.1415), so in 2015 Pi Day will be extra special (3/14/15). If you round pi to the nearest ten thousandth, you get So perhaps Pi Day will be extra special in 2016 as well.
17 The circumference of a circle can be found by finding of the product of π and the length of the diameter. C = πd or C = 2πr
18 The area of a circle can be found by finding of the product of π and square of the length of the radius. = πr 2
19 Theorem 19: ll radii of a circle are congruent.
20 Theorem 19: ll radii of a circle are congruent. Postulate: Two points determine a line (or ray or segment.)
21 Theorem 19: ll radii of a circle are congruent. The definition of a circle states that all points on a circle are the same distance from a given point (the center). Each one of the given points forms a segment with the center, because two points determine a segment. Those segments are all radii by definition. The lengths of the radii are all the same by the definition of a circle, and all segments with the same length are congruent.
22 Given: L Prove: Proof Statement S Reason C
23 Given: L Prove: Proof Statement S Reason C
24 Given: L Prove: Proof Statement S Reason C
25 Given: L Prove: S C Proof Statement Given Reason
26 Given: L Prove: S C Proof Statement Reason Given Given
27 Given: L Prove: S C Proof Statement Reason Given Given 3. LS, LC rt. 's 3. lines form rt. 's T
28 Given: L Prove: S C Proof Statement Reason Given Given 3. LS, LC rt. 's 3. lines form rt. 's 4. LS LC 4. all rt 's ~= T ~=
29 Given: L Prove: S C Proof Statement Reason Given Given 3. LS, LC rt. 's 3. lines form rt. 's 4. LS ~= LC 4. all rt 's ~= 5. S C 5. radii ~= T
30 Given: L Prove: S C Proof Statement Reason Given Given 3. LS, LC rt. 's 3. lines form rt. 's 4. LS ~= LC 4. all rt 's ~= 5. S ~= C 5. radii 6. L L 6. ref. ~= T
31 Given: L Prove: S C Proof Statement Reason Given Given 3. LS, LC rt. 's 3. lines form rt. 's 4. LS ~= LC 4. all rt 's ~= 5. S ~= C 5. radii 6. L ~= L 6. ref. 7. LS LC 7. SS ~= T
32 Given: L Prove: S C Proof Statement Reason Given Given 3. LS, LC rt. 's 3. lines form rt. 's 4. LS ~= LC 4. all rt 's ~= 5. S ~= C 5. radii 6. L ~= L 6. ref. 7. LS ~= LC 7. SS CPCTC T
33 Given: Prove: Proof Statement S Reason B L C
34 Given: Prove: Proof Statement S Reason B L C
35 Given: Prove: Proof Statement S Reason B L C
36 Given: Prove: S L C Proof Statement Given B Reason
37 Given: Prove: S L C Proof Statement Given radii B Reason
38 Given: Prove: S L C Proof Statement B Reason Given radii vertical 's
39 Given: Prove: S L C Proof Statement B Reason Given radii vertical 's radii
40 Given: Prove: S L C Proof Statement B Reason Given radii vertical 's radii 5. SB CL 5. SS ~=
41 Given: Prove: S L C Proof Statement B Reason Given radii vertical 's radii 5. SB ~= CL 5. SS CPCTC
42 Corresponding parts of congruent triangles are congruent. (CPCTC)
43 Corresponding parts of congruent triangles are congruent. (CPCTC) Definition: Circle: circle is the set of all points in a plane the same distance from a given point.
44 Definitions: Radius: radius is a segment with one endpoint on a circle and the other endpoint at the center of the circle.
45 Definitions: Radius: radius is a segment with one endpoint on a circle and the other endpoint at the center of the circle. Chord: segment that has both endpoints on the same circle is a chord.
46 Definitions: Radius: radius is a segment with one endpoint on a circle and the other endpoint at the center of the circle. Chord: segment that has both endpoints on the same circle is a chord. Diameter: chord that passes through the center of a circle is a diameter.
47 The ratio of the circumference to the diameter of all circles is the same. That ratio is called pi (π).
48 The ratio of the circumference to the diameter of all circles is the same. That ratio is called pi (π). The circumference of a circle can be found by finding of the product of π and the length of the diameter. C = πd or C = 2πr
49 The ratio of the circumference to the diameter of all circles is the same. That ratio is called pi (π). The circumference of a circle can be found by finding of the product of π and the length of the diameter. C = πd or C = 2πr The area of a circle can be found by finding of the product of π and square of the length of the radius. = πr 2
50 Theorem 19: ll radii of a circle are congruent.
51 Theorem 19: ll radii of a circle are congruent. Postulate: Two points determine a line (or ray or segment.)
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