G EOMETRY By: 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 (x 2- x 1 )2 + (y 2- y 1 )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 3 ANGLES 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 angles Equiangular: 3 congruent angles Right: 1 right angle Obtuse: 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.

C HAPTER 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 FLOWCHART Quadrilaterals TrapezoidParallelogramKite -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 Over x-axis: (x,y) -> (x,-y) Over y-axis: (x,y) -> (-x,y) Over y=x: (x,y) -> (y,x) Over y=-x: (x,y0 -> (-y,-x) 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 x=75 x=50 x=2

CHAPTER 9 THEOREMS Triangle- the hypotenuse is square root 2 times as long as the short legs 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 x x x=4.2 x=4

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 E FG H I J __ Tangent __ Secant __ Circle __ Common External Tangent __ Common Internal Tangent __ Tangent Circles __ Cocentric Circles __ Radius __ Chord __Diameter

CHAPTER 11 THEOREMS Theorem the sum of the measures of the interior angles of a convex n-gon is (n-12)180. Corollary (n-2)180/n Theorem the sum of the measures of the exterior angles of a convex polygon, one angles at each vertex is 360 degrees. 360/n Theorem the area of an equilateral triangle= square root 3(sxs)/4 Theorem the area of a regular n-gon = 1/2aP

CHAPTER 11 PRACTICE PROBLEMS

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 TetrahedronCubeOctahedronDodecahedronIcosahedron