21 Inductive Reasoning and Conjecture Real Life Vocabulary Inductive Reasoning reasoning that uses a number of specific examples to arrive at your conclusion Conjecture a concluding statement reached using inductive reasoning ID: 191571
Download Presentation The PPT/PDF document "Ms. Andrejko" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Ms. Andrejko
2-1 Inductive Reasoning and ConjectureSlide2
Real - LifeSlide3
Vocabulary
Inductive Reasoning
- reasoning that uses a number of specific examples to arrive at your conclusion
Conjecture-
a concluding statement reached using inductive reasoning
Counterexample-
a false example that can be a number, drawing, or a statement. Slide4
Steps to making a conjecture
1. Find a pattern in the sequence that you are given, or write out examples to find a pattern based on what you are given.
2. Write the pattern that you have found in the form of a conjecture.
IF GIVEN A CONJECTURE: Find a counter example, to prove that it is falseSlide5
Examples
1.
Conjecture: Each figure grows by increasing by 2 shaded diamonds and 1 shaded diamond. The next figure will have a total of 8 shaded diamonds and 5 white diamonds.
2
. -4, -1, 2, 5, 8
Conjecture: Each number is increasing by 3 every time. The next number will be 11.
3. -2, -4, -8, -16, -32
Conjecture: Each number is two times as many as the previous number. The next number will be -64. Slide6
PRACTICE
1.
Conjecture: Each figure grows by 2 dots each time. The next figure will contain 12 dots (5 on each side, and one on the top and bottom)
2
. -5, -10, -15, -20
Conjecture: Each number is decreasing by 5 more each time. The next number in the series will be -25.
3.
Conjecture: Each number is being multiplied by - ½ . The next number will be 1/16. Slide7
Examples – Make a conjecture about the geometric relationships
4
. N is the midpoint of QP
Conjecture: QN
≅
NP
5. <3
≅
<4
Conjecture: < 3 and < 4 are vertical angles
6
. <1, <2, <3, <4 form 4 linear pairs
Conjecture: <1 and < 3 are vertical angles, <2 and angle 4 are vertical angles
1
2
3
4Slide8
PRACTICE– Make a conjecture about the geometric relationships
4
. <ABC is a right angle.
Conjecture: < ABC = 90°
5. ABCD is a parallelogram
Conjecture: ABCD has 4 sides
6
.
Conjecture: PQRS is a squareSlide9
Examples – T or F - Counterexamples
7. If <ABC and <CBD form a linear pair, then <ABC
≅
<CBD
8. If AB, BC, and AC are congruent, then A, B, and C are collinear
9. If AB + BC = AC, then AB = BC
20
160
Counterexample:
Counterexample:
A
B
C
Counterexample:
10 + 20 = 30 , but 10 ≠ 20.
A
B
C
---- 10 ----
-------- 20 --------
---------------- 30 ---------------Slide10
PRACTICE– T or F - Counterexamples
7. If <1 and <2 are adjacent angles, then <1 and <2 form a linear pair
8. If S,T, and U are collinear, and ST = TU, then T is the midpoint of SU
9. If
n
is a real number, then n
2
>
n
Counterexample:
0
2
= 0 ; 1
2
= 1 ; ( ½)
2
= (¼)
1
2
Counterexample:
TRUE