Midterms Study Tool

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Chapter 1: Basics of Geometry

We learned how to...

Find and describe patterns.

Use inductive reasoning.

Use defined and undefined terms.

Sketch intersections of lines and planes.

Use segment postulates and the Distance Formula.

Use angle postulates and classify angles.

Bisect a segment and an angle.

Identify vertical angles, linear pairs, complementary angles, and supplementary angles.

Find the perimeter, circumference, and area of common plane figures.

Use a general problem-solving plan.

Words to Remember...

Visual Patterns

Numerical Patterns

Inductive reasoning: Looking for a pattern to make a conjecture

Conjecture: rule or unproven statement based on observations

Counterexample: shows the conjecture to be false

Point, Line, Plane, Line Segment, Ray, Intersections, Collinear, Coplanar

Theorem: a rule that is accepted because of logical proof

Postulate: a rule that is accepted without proof, until counterexample is found.

Interior, Exterior, Vertex, Congruent Angles, Equivalent Angles

Adjacent Angles: share a vertex and a side.

Bisector: divides things into two congruent parts

Supplementary Angles, Complementary Angles, Vertical Angles, Linear Pair

Theorems...

Pythagorean Theorem: In a right triangle, should be exact and simplified.

Postulates...

Segment Addition Postulate

Ruler Postulate

Protractor Postulate: similar to ruler postulate

Angle Addition Postulate

Formulas...

Distance Formula: SUBTRACTION, not addition! order of points doesn't matter, keep consistent

Midpoint Formula: AVERAGE x's, then y's over 2