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