Geometr!zzle is Everywh!zzLe

GEOMETR!ZZLE IS EVERYWH!ZZLEJ-Kizzle and R-FizzleMr. Sal-Gizzle`s Class

If P is in the interior of ∠RST, then m∠RST = m∠RSP + m∠PST.

Ch1 Angle Addition Postulate

If B is between A and C, then AB + BC = AC

Ch1 Segment Addition Postulate

If there is a line and a point not on the line then there is exactly one line through the point perpendicular to the given line.

Ch2 Perpendicular Postulate

All right angles are congruent.

∠G ≅ to ∠Y

Ch2 Right Angles Congruence Theorem

If there is a line and a point not on the line then there is exactly one line through the point parallel to the given line.

Ch3 Parallel Postulate

If 2 parallel lines are cut by a transversal, then the corresponding angles are congruent

Ch3 Corresponding Angles Converse

If 2 sides of a triangle are congruent then the angles opposite them are congruent.

Ch4 Base Angles Theorem

If two angles of a triangle are congruent, the sides opposite them are congruent.

Ch4 Triangle Sum Theorem

In a plane, if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Ch5 Perpendicular Bisector Theorem

The sum of the lengths of any 2 sides of a triangle is greater than the length of the third side. (A + B > C , B + C > A , C + A > B)

Ch5 Triangle Inequality Theorem

If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths.

( EF+ FH + HG + GE EF FH HG GE

Ch6 Perimeter of Similar Polygons

A B

C D

E

G

F

H

AB + BD + DC + CA AB BD DC CA= = = =

If two angles of one triangle are congruent to two angles of another triangle, then the

two triangles are similar

▲ABC ~ ▲DEF

Ch6 AA Similarity Postulate

A2 + B2 = C2

Ch7 Pythagorean Theorem

In a 45-45-90 triangle the hypotenuse is 2 times as long as each leg.

Ch8 45-45-90 Triangle Theorem

45

45

x

x

X √2

A quadrilateral is a rhombus if and only if it has four congruent sides.

Ch8 Rhombus Corollary

A translation is an isometry

Ch9 Translation Theorem

A reflection is an isometryCh9 Reflection Theorem

The measure of an arc formed by 2 adjacent arcs is the sum of the measures of the 2 arcs.

Ch 10 Arc Addition Postulate

In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

Ch10 Theorem 10.3

The area of a rectangle is the product of its base.

A = bh

Ch11 Area of a Rectangle

b

h

The area of a square is the square of the length of its side or

A = S2

Ch11 Area of A Square Postulate

F + V = E + 2

6 + 8 = 12 + 214 = 14

Ch12 Euler’s Theorem

the volume of a Cube is the cube of the length of its side or V=S^3

Ch12 Volume of A Cube