Chapter 6: Geometry

Exterior Angle Inequality Thm.

The measure of an exterior angle of a triangle is greater than the measure of either remote interior angles

Adding 2 big things will still be bigger than adding to smaller things

If a>b and c ≥ d, then a+c > b+d

If a is bigger than b, and c is greater than 0, then a divided by c is greater than b divided by c

if a > b and c>0, then a/c > b/c

if one number is bigger than the other number and the third number is less than 0, then the first number times the third number will always be less than the second number times the third. And the first number divided by the third number will be smaller than the second number divided by the third.

if a > b and c < 0, then ac< bc and a/c < b/c

if the first number is greater than the second number, and the second number is greater than the third number, then the first number is greater than the third number

if a > b and b > c, then a > c

if the first number, a, is equal to the sum of 2 numbers and the 3rd number is greater than zero, then the 1st number is greater than the second number and the third number

if a = b + c and c > 0, then a > b and a > c

Statement

if p then q

Inverse

if NOT P then NOT Q

Contrapositive

if NOT Q then NOT P

A statement and its contrapositive are always…

Logically equivalent statements

A statement is NOT logically equivalent to its….

Converse or Inverse

Triangle inequality thm.

if ONE SIDE of a triangle is LONGER THAN A SECOND SIDE, then the ANGLE OPPOSITE TO THE FIRST SIDE is LARGER than the ANGLE OPPOSITE TO THE SECOND SIDE

Triangle Inequality Thm.

if ONE ANGLE of a triangle is LARGER THAN A SECOND ANGLE then the SIDE OPPOSITE to the FIRST ANGLE is LONGER than the SIDE OPPOSITE TO THE SECOND ANGLE

Corollary 1

The perpendicular segment from a point to a LINE is the shortest segment from the point to the LINE

Corollary 2

The perpendicular segment from a point to a PLANE is the shortest segment from the point to the PLANE

Thm 6.4

The SUM of the lengths of any two sides of a triangle is greater than the length of the third side.

SAS Inequality Thm

if TWO SIDES of one triangle are congruent to TWO SIDES OF ANOTHER triangle, but the included ANGLE of the FIRST TRIANGLE IS LARGER THAN the included angle of the SECOND TRIANGLE, then the THIRD SIDE of the first triangle is LONGER than the THIRD SIDE of the SECOND ( you should be given ANGLES and sides to use this)

SSS Inequality Thm

If TWO SIDES of one triangle are congruent to TWO SIDES of another triangle, but the THIRD SIDE of the FIRST TRIANGLE is LONGER than the THIRD SIDE OF THE SECOND TRIANGLE then the included ANGLE of the first is LARGER than the INCLUDED ANGLE OF THE SECOND TRIANGLE.