Geometry Notes

Section 2-1

9/20/07

What you’ll learn

How to make conjectures based on inductive reasoning

How to find counterexamples

Vocabulary

Conjecture Inductive reasoning Counterexample

Conjecture

An educated guess

Make a conjecture Given: lines l and m are

perpendicular

Conjecture: lines l and m form adjacent angles

Conjecture: lines l and m form right angles

Conjecture: lines l and m form congruent, adjacent angles

Inductive Reasoning

An argument using many examples to support the conjecture

Counterexamples

A false example An example that contradicts the

statement

Use inductive reasoning to find the next two terms in each sequence. 4, 8, 12, 16, _____, _____ 400, 200, 100, 50, 25, _____, _____ 1/8, 2/7, ½, 4/5, _____, _____ -5, 3, -2, 1, -1, 0, _____, _____ 360, 180, 120, 90, _____, _____ 1, 3, 9, 27, 81, _____, _____ 1, 5, 17, 53, 161, _____, _____ 1, 5, 14, 30, 55, _____, _____

20 2412.5 6.25

5/4 2

-1 -172 60

243 729485 1457

91 140

True or False? If false give a counter example. . . Given: m + y > 10, y > 4 Conjecture: m< 6

Try a number for m that would contradict your conjecture

Conjecture: m< 6 so let’s try m = 7 7 + 4* > 10 *remember: y > 4 11> 10

Is a true statement so our conjecture is false.

True or False? If false give a counter example. . . Given: AM = MP Conjecture: M is the midpoint of AP

What might a counterexample look like? Does it say M is between A and P? No

A P

M

Given AM = MP, M is not always the mdpt of AP

True or False? If false give a counter example. . . Given: A(-4, 8), B(3,8), C(3, 5) Conjecture: ΔABC is a right triangle

How would you know if it is a right triangle?Use the distance formula to find AB, BC, and ACThen see if those measures work in the pythagorean theorem

True or False? If false give a counter example. . . Given: noncollinear points R, S, and T Conjecture: RS, ST, and RT form a

triangle Through any two points there is a unique line

RS, ST, and RT would have to make a triangle

Have you learned?

How to make conjectures based on inductive reasoning?

How to find counterexamples?

Assignment P. 64 (11-67odd) & Notes 2-2