Inequalities And Indirect Proof

Front 1

The Exterior Angles Inequality Theorem

Back 1

The measure of an exterior angle of a triangle is greater than the measure of either remote (non-adjacent) interior angle.

Front 2

if p, then q

Back 2

Conditional Statement

Front 3

If not p, then not q

Back 3

Inverse

Front 4

If q, then p

Back 4

Converse

Front 5

If not q, then not p

Back 5

Contrapositive

Front 6

Indirect Proof

Back 6

1) Assume temporarily that the conculsion is not true.
2) Reason logically until you reach a contradiction of a known fact.
3) Point out that the temporary assumption must be false, and that the conclusion must then be true.

Front 7

Opposite Sides Theorem

Back 7

If one side of a traignle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side.

Front 8

Opposite Sides Converse Theorem

Back 8

If one angle of a triangle is larger than a second angle, then the side opposite the first angle is longer than the side opposite the second angle.

Front 9

Corollary 1 to the Opposite Sides Theorem (Line)

Back 9

The perpendicular segmentfrom a point to a line is the shortest segment from the point to the line.

Front 10

Corollary 2 to the Opposite Sides Theorem (Plane)

Back 10

The perpendicular segment from a point to a plane is the shortest segment from the point to the plane.

Front 11

The Triangle Inequality Theorem

Back 11

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

Front 12

Side-Angle-Side (SAS) Inequality Theorem

Back 12

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, then the third side of the first triangle is longer than the third side of the second traingle.

Front 13

Side-Side-Side (SSS) Inequality Theorem

Back 13

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, then the included angle of the first triangle is larger than the included angle of the second.

Front 14

Properties of Inequalities

Back 14

[>= means greater than or equal to.
<= means less than or eqaul to.]
If a > b and c >= d, then a + c > b + d.
If a > b and c > 0, then ac > bc, and (a/c) > (b/c).
If a > b and c < 0, then ac < bc, and (a/c) > (b/c).
If a > b and b > c, then a > c (Transative Property).
If a = b + c and c > 0, then a > b.

Front 15

What is a biconditional Statment

Back 15

The combining of a conditional statement and its converse, or the inverse and contrapositive. When the two are combined you use the phrase " if and only if".