Geometry Review

Morgan Parsons

Honors Geometry Mrs. Lowe

June 2, 2009

Formulas: Square A= S²P = 4s

Triangle P = a + b +

c A = ½ bh

a b

c

Rectangle

P = 2L + 2wA= Lw

w

L

CircleC = 2 rA = r²

Tips for Next years students: know your formulas! Knowing the formulas makes things easier as your geometry gets harder.

-Parallel lines are two lines that are coplanar and do not intersect.

-Perpendicular lines are two lines that intersect to form a right angle

Corresponding Angles PostulateIf two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

1

2

Example:1 2

Two figures are congruent if they have exactly the same size and shape.

SSS Congruence Postulate – If 3 sides of one triangle are congruent to the three sides of a second triangle, then the two triangles are congruent.

SAS Congruence Postulate – If 2 sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.

ASA Congruence Postulate – If 2 angles & the included side of one triangle are congruent to 2 angles & the included side of a second triangle, then the 2 triangles are congruent.

AAS Congruence Theorem – If 2 angles & a non-included side of one triangle are congruent to 2 angles & the corresponding non-included side of a second triangle, then the two triangles are congruent.

Chapter 61

2

3

4

Theorem 6.1 Interior Angles of a Quadrilateral

The sum of the measures of the interior angles of a quadrilateral is 360

m1 + m2 + m3 + m4 = 360

Corollaries About Special Quadrilaterals

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

Rectangle Corollary A quadrilateral is a rectangle if and only if it has four right angles.

Square CorollaryA quadrilateral is a square if and only if it is a rhombus and a rectangle.

Chapter 7 Reflection – Where the line acts like a mirros, with an image reflected in the line.

Rotation – Transformation in which a figure is turned around a fixed point.

Translation - a transformation that maps every two points P and Q in the plane to points P’ and Q’, so that the following properties are true.

1. PP’ = QQ’2. PP’ || QQ’, or PP’ and QQ’ are collinear.

P’

Q’

P

Q

Chapter 8When there is a correspondence between two polygons such that their corresponding angles are congruent and the lengths of corresponding sides are proportional the two polygons are called similar polygons.

AA Similarity PostulateIf two angles of one triangle are

congruent to two angles of another triangle, then the two triangles are

similar.

SSS Similarity TheoremIf the lengths of the corresponding sides of two triangles are proportional, then the triangles are

similar.

SAS Similarity TheoremIf an angle of one triangle is congruent to an angle of a second triangle and the lengths of

the sides are proportional then the triangles are similar.

Chapter 9Right triangles whose angle measures are 45 -45 -90 or 30 -60 -90

are called special right triangles.

45-45-90 Triangle TheoremIn a 45-45-90 triangle, the hypotenuse is 2 times as long as each leg.

45

45

x

x

2x

Hypotenuse = 2 leg

30-60-90 Triangle TheoremIn a 30-60-90 triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is 3 times as the shorter leg.

60

30x

3x

2x

Hypotenuse = 2 shorter legLonger leg =3 shorter leg

Chapter 10

Center

Diameter

Radius

chord

Secant

Chapter 11

Circumference of a circle = 2r

Arc Length CorollaryIn a circle, the ratio of the length of a given arc to the circumference is equal to the ratio of the measure of the arc to 360Arc length of AB

2 r= mAB

360

Area of a circle = r2

Area of a SectorThe ratio of the area A of a sector of a circle to the area of a circle is equal to the ratio of the measure of the intercepted arc to 360

A mABr 360=2

Chapter 12Volume Postulates

Postulate 27 Volume of a cubeThe volume of a cube is the cube of the length of its side, or v = s³

Postulate 28 Volume Congruence PostulateIf two polyhedra are congruent, then they have the same volume.

Postulate 29 Volume Addition PostulateThe volume of a solid is the sum of the volumes of all its non-overlapping parts.

Euler’s TheoremThe number of faces (F), vertices (V), and edged (E) of a polyhedron are related by the formula F + V = E = 2.

THE END

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