Adv. Geo. Unit 3

Proofs in Coordinate Geometry

1. Involve ideas from Algebra 2. Often nearly automatic (involving a little more than a few calculations.)

Sufficient Conditions for Parallelograms

1. If both pairs of opposite sides are congruent then the quadrilateral is a parallelogram. (Distance formula) 2. If both pairs of opposite angles are congruent then the quadrilateral is a parallelogram. (Square/ Rectangle 90 degrees) 3. If the diagonals bisect each other then the quadrilateral is a parallelogram. (Midpoint Formula) 4.If one pair of opposite sides are both congruent and parallel then the quadrilateral is a parallelogram. (Slopes are congruent)

Law of Contrpositive

A conditional and it contrapositive is either both true or both false.

Indirect Reasoning

A person examines and tries to rule out all the possibilities other than the ones thought to be true.

Indirect Proofs

A proof whose argument uses every Law.

Indirect Arguments

Assuming facts are true, claiming something impossible, then because it is impossible claiming that the facts are false.

CPCTC

Corresponding Parts of Congruent Triangles are Congruent. You must know that the triangles are congruent to use this.

You avoid using fractions when your calculate the midpoint.

Explain why it might be useful to assign 2p as a coordinate instead of just p?

Overlapping Figures

Figures that share common vertices, sides, and angles.

The way your position it will affect your coordinates.

How does the way you position a figure in the coordinate plane affect your calculations in a coordinate proof?

ASA congruence Theorem

If 2 angles and the included side of 1 triangle are congruent to 2 angles and the included side of another triangle then the triangles are congruent.

AAS Congruence Theorem

If 2 angles and the non-included side of 1 triangle are congruent to 2 angles and the non-included side of another triangle then the triangles are congruent.

SAS Congruence Theorem

If 2 sides and the included angle of 1 triangle are congruent to 2 sides and the included angles of another triangle then the triangles are congruent.

SSS Congruence Theorem

If 3 sides of 1 triangle are congruent to 3 sides of another triangle then they are congruent.

HL Congruence Theorem

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another triangle then the triangles are congruent.

SsA Condition

If two sides and the angle opposite the longer of the two sides in one triangle are congruent to two sides and the angle opposite the longest of the two sides in another triangle then the triangles are congruent.

Law of Indirect Reasoning

If valid reasoning from a statement (p) leads to a false conclusion, then p is false.

Convenient Locations

Is one in which its key points are described with the fewest possible numbers of variables.

Proofs in Synthetic Geometry

These proofs involve points as locations.

Law of Ruling out Possibilities

When a statement p or statement q is true, and q isn't true, then p is true.

You don't know the numbers, numbers make it specific which limits yourself, variables makes it broader.

When writing a coordinate proof why are variables used instead of numbers as coordinates for the vertices of a figure?