GEOMETRYBy: Chelsea Ralph

CHAPTER 1 TERMS

Conjecture- an unproven statement based on observations

Counterexample-shows a conjecture is false Complementary Angles- angles that sum up

to 90 degrees Supplementary Angles- angles that sum up

to 180 degrees

CHAPTER 1 THEOREMS

Distance formula- square root of (x2-x1)2 + (y2-y1)2 Ex- find the distance of (1,2) (3,5)

Pythagorean Theorem- a2+b2=c2 Ex- find c if a=3 and b=4

Midpoint- (x+x/2, y+y/2) Ex- find the midpoint of (4,6) (8,8)

CHAPTER 3 TERMS

Parallel lines- two lines that are coplanar and don’t intersect

Skew lines- two lines that are not coplanar and don’t intersect

Transversal- a line that intersects two or more coplanar lines

CHAPTER 3ANGLES FORMED BY A TRANSVERSAL

1 and 5 are corresponding angles

1 and 7 are alternate interior angles

4 and 6 are alternate interior angles

4 and 5 are consecutive interior angles

1 and 3 are vertical angles

6 and 7 are adjacent angles

CHAPTER 3 THEOREMS

Theorem 3.1- if two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular

Theorem 3.2-if two sides of two adjacent acute angles are perpendicular, then the angles are complementary

Theorem 3.3- if two lines are perpendicular, then they intersect to form four right angles

Slopes of Perpendicular Lines- in a coordinate plane, two non-vertical lines are perpendicular in the product of their slopes is -1

CHAPTER 4 TRIANGLES

Classified by Angles:Acute: 3 acute anglesEquiangular: 3 congruent anglesRight: 1 right angleObtuse: 1 obtuse angle

Classified by Sides:

Equilateral: 3 congruent sides

Isosceles: 2 congruent sides

Scalene: no congruent sides

CHAPTER 4 POSTULATES

Side-Side-Side- if three sides of one triangle are congruent to the three sides of a second triangle, then the two triangles are congruent.

Side-Angle-Side- if two sides and the included angle of one triangle are congruent to two sides and the included angles of a second triangle, then the two triangles are congruent.

Angle-Side-Angle- if two angles and the included side of one triangles are congruent to two angles and the included side of a second triangle, then the two triangles are congruent.

CHAPTER 4 POSTULATES (CONT.)

Angle-Angle-Side- if two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of a second triangle, then the two triangles are congruent.

Hypotenuse-Leg- if the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.

CHAPTER 6 TERMS

Polygon- a plane figure that is formed by three or more segments called sides and that each side intersects exactly two other sides, one at each endpoint.

Regular- a polygon that is equiangular and equilateral.

Convex- a polygon that has no line that contains a side of the polygon in the interior.

Concave- a polygon that is not convex.

CHAPTER 6 FLOWCHARTQuadrilaterals

Trapezoid Parallelogram Kite

-exactly one pair of parallel sides

-both pairs of opposite sides are congruent and parallel-opposite angles are congruent-angle is supplementary to consecutive interiors-diagonals bisect

-consecutive sides are congruent-exactly one pair of congruent angles-diagonals are perpendicular

Isosceles Trapezoid-non parallel sides are congruent-base angles are congruent

Rectangle-four right angles-diagonals congruent

Right Trapezoid-two right angles

Rhombus-four congruent sides-diagonals perpendicular

Square-four right angles-four congruent sides-diagonals congruent-diagonals perpendicular

CHAPTER 7 TERMS

Preimage- original figure Image- new figure Transformation-operation that moves the

preimage into the image Isometry- a transformation that preserves its

lengths

CHAPTER 7 TRANSFORMATIONS

Reflection Rotation Translation

90 clockwise: (x,y) -> (y,-x)180 clockwise: (x,y) -> (-x,-y)270 clockwise: (x,y) -> (-y,x)

(x,y) -> (x+h,y+k)

CHAPTER 8 TERMS

Proportion- an equation that equates two ratios

Ratio-a comparison of two numbers Similar polygons- a correspondence between

two polygons such that their corresponding angles are congruent and the lengths of corresponding sides are proportional

Dilation- nonrigid transformation that reduces or enlarges the preimage

Geometric mean- a/x = x/b

CHAPTER 8 PRACTICE PROBLEMS

3/2=x/4

3/9=1/x

x/15=5/1

100/x=x/25

1/x=x/4

x=6

x=3

CHAPTER 9 THEOREMS

45-45-90 Triangle- the hypotenuse is square root 2 times as long as the short legs

30-60-90 Triangle- the hypotenuse is twice the length of the short leg and the long leg is square root 3 times longer than the short leg

Trigonometric ratios Sine=opposite/hypotenuse Cosine= adjacent/hypotenuse Tangent= opposite over adjacent

CHAPTER 9 PRACTICE PROBLEMS

Find x

3

3 x8

6.9

x

CHAPTER 10 TERMS

Circle- the set of all points in a plane that are equidistant from a given point

Radius-the distance from the center of the circle to a point on the circle

Diameter- the distance across the circle, through the center

Chord- segment whose endpoints are on the circle

Secant- a line that intersects the circle in two points

Tangent- a line in the plane of the circle that intersects the circle in one point

CHAPTER 10 TERMS (CONT.)

Tangent circles- coplanar circles that intersect in one point called tangent circles

Cocentric circles- coplanar circles that have a common center

Common tangent- a line that is tangent to two circles

Common internal tangent- intersects the segment that joins the centers of the circle

Common external tangent- does not intersect the segment joining the circles

CHAPTER 10 PIECING IT TOGETHER

A

B

C

D

EFG

H

I

J

__ Tangent__ Secant__ Circle__ Common External Tangent__ Common Internal Tangent__ Tangent Circles__ Cocentric Circles__ Radius__ Chord__Diameter

CHAPTER 11 THEOREMS

Theorem 11.1- the sum of the measures of the interior angles of a convex n-gon is (n-12)180. Corollary (n-2)180/n

Theorem 11.2- the sum of the measures of the exterior angles of a convex polygon, one angles at each vertex is 360 degrees. 360/n

Theorem 11.3- the area of an equilateral triangle= square root 3(sxs)/4

Theorem 11.4- the area of a regular n-gon = 1/2aP

CHAPTER 11 PRACTICE PROBLEMS

10

15

CHAPTER 12 TERMS

Polyhedron- a solid that is bounded by polygons

Platonic solids- Tetrahedron- 4 faces, 4 vertices, 6 edges Cube-6 faces, 8 vertices, 12 edges Octahedron- 8 faces, 6 vertices, 12 edges Dodecahedron- 12 faces, 20 vertices, 30 edges Icosahedron- 20 faces, 12 vertices, 30 edges

CHAPTER 12 MATCHING

Tetrahedron Cube Octahedron Dodecahedron Icosahedron