Geometr!zzle is Everywh!zzLe
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Transcript of 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