Geometry Vocabulary Semester 2

Front 1

Polygon Angle-Sum Theorem

Back 1

The sum of the measures of the angles of an n-gon is (n-2)180.

Front 2

Corollary to the Polygon Angle-Sum Theorem

Back 2

The measure of each angle of a regular n-gon is ((n-2)180)/2.

Front 3

Polygon Exterior Angle-Sum Theorem

Back 3

The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.

Front 4

Theorem 6-3

Back 4

If a quadrilateral is a parallelogram, then its opposite sides are congruent.

Front 5

Theorem 6-4

Back 5

If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

Front 6

Theorem 6-5

Back 6

If a quadrilateral is a parallelogram, then its opposite angles are congruent.

Front 7

Theorem 6-6

Back 7

If a quadrilateral is a parallelogram, then its diagonals bisect each other.

Front 8

Theorem 6-7

Back 8

If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

Front 9

Theorem 6-8

Back 9

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Front 10

Theorem 6-9

Back 10

If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram.

Front 11

Theorem 6-10

Back 11

If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Front 12

Theorem 6-11

Back 12

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Front 13

Theorem 6-12

Back 13

If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.

Front 14

Theorem 6-13

Back 14

If a parallelogram is a rhombus, then its diagonals are perpendicular.

Front 15

Theorem 6-14

Back 15

If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles.

Front 16

Theorem 6-15

Back 16

If a parallelogram is a rectangle, then its diagonals are congruent.

Front 17

Theorem 6-16

Back 17

If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

Front 18

Theorem 6-17

Back 18

If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus.

Front 19

Theorem 6-18

Back 19

If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

Front 20

Theorem 6-19

Back 20

If a quadrilateral is an isosceles trapezoid, then each pair of base angles is congruent.

Front 21

Theorem 6-20

Back 21

If a quadrilateral is an isosceles trapezoid, then its diagonals are congruent.

Front 22

Trapezoid Midsegment Theorem

Back 22

If a quadrilateral is a trapezoid, then the midsegment is parallel to the bases, and the length of the midsegment is half the sum of the lengths of the bases.

Front 23

Theorem 6-22

Back 23

If a quadrilateral is a kite, then its diagonals are perpendicular.

Front 24

Midpoint Formula

Back 24

(x-sub 1 minus x-sub 2 over 2, y-sub 1 minus y-sub 2 over 2)

Front 25

Slope Formula

Back 25

y-sub 1 minus y-sub 2 over x-sub 1 minus x-sub 2

Front 26

Distance Formula

Back 26

The square root of (x-sub 2 minus x-sub 1)^2 plus (y-sub 2 minus y-sub 1)^2

Front 27

Cross Products Property

Back 27

In a proportion, the product of the extremes equals the products of the means.

Front 28

Properties of Proportions (1)

Back 28

If both sides of a proportion are reciprocated, then they are still equal.

Front 29

Properties of Proportions (2)

Back 29

If the means of a proportion are switched, then the proportion is still equal.

Front 30

Properties of Proportions (3)

Back 30

If the denominator is added to the numerator of a proportion, then the proportion is still equal.

Front 31

Similar Polygons

Back 31

Two polygons are similar polygons if corresponding angles are congruent and if the lengths of corresponding sides are proportional.

Front 32

Angle-Angle Similarity (AA~) Postulate

Back 32

If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Front 33

Side-Angle-Side Similarity (SAS~) Theorem

Back 33

If an angle of one triangle is congruent to an angle of a second triangle, and the sides that include the two angles are proportional, then the triangles are similar.

Front 34

Side-Side-Side Similarity (SSS~) Theorem

Back 34

If the corresponding sides of two triangles are proportional, then the triangles are similar.

Front 35

Theorem 7-3

Back 35

The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other.

Front 36

Corollary 1 to Theorem 7-3

Back 36

The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse.

Front 37

Corollary 2 to Theorem 7-3

Back 37

The altitude to the hypotenuse of a right triangle seperates the hypotenuse so that the length of each leg of the triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to the leg.

Front 38

Side-Splitter Theorem

Back 38

If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.

Front 39

Corollary to the Side-Splitter Theorem

Back 39

If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional.

Front 40

Trianle-Angle-Bisector Theorem

Back 40

If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.

Front 41

Pythagorean Theorem

Back 41

If a triangle is a right triangle, then c^2=a^2+b^2.

Front 42

Converse of the Pythagorean Theorem

Back 42

If c^2=a^2+b^2, then the triangle is a right triangle.

Front 43

Theorem 8-3

Back 43

If c^2>a^2+b^2, then the triangle is obtuse.

Front 44

Theorem 8-4

Back 44

If c^2

Front 45

45-45-90 Triangle Theorem

Back 45

In a 45-45-90 triangle, both legs are congruent and the length of the hypotenuse is the square root of 2, times the length of the leg.

Front 46

30-60-90 Triangle Theorem

Back 46

In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shorter leg. The length of the longer leg is the square root of 3, times the length of the shorter leg.

Front 47

Translation

Back 47

A transformation that maps all point of a figure the same distance in the same direction

(If triangle ABC is translated to become triangle A'B'C', you would write T(Triangle ABC)=Triangle A'B'C').

Front 48

Reflection

Back 48

A transformationin which all points of a figure are reflected across a line, known as the line of reflection, with these two properties:

-If point A is on the line of reflection, then the image of A is itself (A'=A).

-If point B is not on the line of reflection, then the line of reflection is the perpendicular bisector of segment BB'.

You would write a reflection across the line of reflection (m) that takes P to P' as Rm(P)=P'.

Front 49

Reflections Preserve Distance

Back 49

If Rm(A)=A', and Rm(B)=B', then AB=A'B'.

Front 50

Reflections Preserve Angle Measure

Back 50

If Rm(

Front 51

Reflections Map Each Point of the Preimage to One and Only One Corresponding Point of Its Image

Back 51

Rm(A)=A' if and only if Rm(A')=A.

Front 52

Rotation About a Point

Back 52

A rotation of x degrees about a point Q, called the center of rotation is a transformation with these two properties:

-The image of Q, center of rotation, is itself (that is, Q'=Q)

-For any other point V, QV'=QV and m

Rotations can be written as r(x degrees, Q)(Triangle UVW)=Triangle U'V'W'

Front 53

Angle of Rotation

Back 53

The number of degrees a figure rotates

Front 54

90 Degree, 180 Degree, 270 Degree, and 360 Degree Rotations

Back 54

-(x, y)=(-y, x)

-(x, y)=(-x, -y)

-(x, y)=(y, -x)

-(x, y)=(x, y)

Front 55

Theorem 9-1

Back 55

The composition of two or more isometries is an isometry.

Front 56

Theorem 9-2 (Reflections Across Parallel Lines)

Back 56

A composition of reflections across two parallel lines is a translation. This composition can be written as (Rm ○ Rl)(Triangle ABC)=Triangle A"B"C" or Rm(Rl(Triangle ABC))=Triangle A"B"C".

-Segment AA", BB", and CC" are all perpendicular to lines l an m.

Front 57

Theorem 9-3 (Reflections Across Intersecting Lines)

Back 57

A composition of reflections across two intersecting lines is a rotation. This composition can be written as (Rm ○ Rl)(Triangle ABC)=Triangle A"B"C" or Rm(Rl(Triangle ABC))=Triangle A"B"C".

-The figure is rotated about the point where the two lines intersect.

Front 58

Congruent Figures

Back 58

Two figures are congruent if and only if there is a sequence of one or more rigid motions that maps one figure onto the other.

Front 59

Dilation

Back 59

A dilation with center of dilation C and scale factor n, n>0, can be written as D(n, C). Dilations preserve angle measure.

Front 60

Similar Figures

Back 60

Two figures are similar if and only if there is a similarity transformation that maps one figure onto the other.

Front 61

Postulate 10-1

Back 61

If two figures are congruent, then their areas are equal.

Front 62

Theorem 10-6

Back 62

The area of a regular polygon is half the product of the apothem and the perimeter.

A=1/2ap

Front 63

Theorem 10-4

Back 63

The area of a trapezoid is half the product of the height and the sum of the bases.

A=1/2h(b1+b2)

Front 64

Theorem 10-5

Back 64

The area of a rhombus or a kite is half the product of the length of its diagonals.

A=1/2d1d2

Front 65

Area of a Rectangle/Parallelogram

Back 65

A=bh

Front 66

Area of a Triangle

Back 66

A=1/2bh

Front 67

Arc Measure

Back 67

The measure of a minor arc is equal to the measure of its corresponding central angle. The measure of the major arc is the measure of the related minor arc subtracted from 360. the measure of a semicircle is 180.

Front 68

Arc Addition Postulate

Back 68

The measure of the arc formed by two adjacent arcs is the sum of the measure of the two arcs.

Front 69

Circumference of a Circle

Back 69

C=(PI)d or C=2(PI)r

Front 70

Arc Length

Back 70

Arc Measure/360*2(PI)r or Arc Measure/360*(PI)d

Front 71

Area of a Circle

Back 71

A=(PI)r^2

Front 72

Area of a Sector of a Circle

Back 72

Arc Measure/360*(PI)r^2

Front 73

Area of a Segment

Back 73

Area of a Sector-Area of the Triangle within the Sector=Area of a Segment

Front 74

L.A. of a Prism

Back 74

ph

Front 75

SA of a Prism

Back 75

ph+b

Front 76

L.A. of a Cylinder

Back 76

2(PI)rh or (PI)dh

Front 77

SA of a Cylinder

Back 77

2(PI)rh+2(PI)r^2

Front 78

L.A. of a Pyramid

Back 78

1/2pl

Front 79

SA of a Pyramid

Back 79

1/2pl+b

Front 80

L.A. of a Cone

Back 80

(PI)rl

Front 81

SA of a Cone

Back 81

(PI)rl+(PI)r^2

Front 82

Volume of a Prism

Back 82

V=Bh

Front 83

Volume of a Cylinder

Back 83

(PI)r^2h

Front 84

Areas and Volumes of Similar Solids

Back 84

If the scale factor fo two similar solids is a:b:

-the ratio of their corresponding areas is a^2:b^2

-the ratio of their volumes is a^3:a^3

Front 85

Volume of a Pyramid

Back 85

V=1/3Bh

Front 86

Volume of a Cone

Back 86

V=1/3(PI)r^2h

Front 87

S.A. of a Sphere

Back 87

S.A.=4(PI)r^2

Front 88

Volume of a Sphere

Back 88

4/3(PI)r^3

Front 89

Area of a Triangle Given SAS

Back 89

Area of Triangle ABC=1/2bc(sinA)

Front 90

Sine

Back 90

o/h

Front 91

Cosine

Back 91

a/h

Front 92

Tangent

Back 92

o/a

Front 93

Law of Sines

Back 93

SinA/a=SinB/b=SinC/c

Front 94

Law of Cosines

Back 94

a^2=b^2+c^2-2bcCosA

Front 95

Theorem 12-1

Back 95

If a line is tangent to a circle, then the line is perpendicular to the radius at the point of tangency.

Front 96

Theorem 12-2

Back 96

If a line in the plane of a circle is perpendicular to a radius at its endpoint on the circle, then the line is tangent to the circle.

Front 97

Theorem 12-3

Back 97

If two tangent segments to a circle share a common endpoint outside the circle, then the two segments are congruent.