Geometry Definitions, Chapter 4

Front 1

congruence

Back 1

Two figures that have the same size and shape

Front 2

Origin

Back 2

The starting point, O

Front 3

coordinates

Back 3

numbers assigned to points using ruler

Front 4

one-dimensional coordinate system

Back 4

choosing an origin and ruler gives this

Front 5

two-dimensional coordinate system

Back 5

used to locate points in a plane. Begin with origin and two perpendicular lines, establish coordinates with ruler

Front 6

axes

Back 6

perpendicular lines

Front 7

x-axis

Back 7

horizontal axis

Front 8

y-axis

Back 8

vertical axis

Front 9

quadrants

Back 9

axes divide plane into 4 of these. Quadrant I is all positive, move counter-clockwise

Front 10

two coordinates

Back 10

locate a point in the plane

Front 11

The Distance Formula

Back 11

The distance between the points P1 (x1, y1) and P2 (x2, y2) is SquareRoot of (x2 – x1) squared + (y2 – y1) squared

Front 12

The Distance Formula

Back 12

given to us by Pathagorean Theorem

Front 13

polygon

Back 13

connected set of at least three line segments in the same plane such that each segment intersects exactly two others, one at each endpoint

Front 14

sides of polygons

Back 14

the line segments

Front 15

vertices of polygons

Back 15

endpoints of line segments

Front 16

polygon always has same number of

Back 16

sides and vertices

Front 17

congruent triangles

Back 17

Two triangles are congruent iff there is a correspondence between their vertices such that all of their corresponding sides and angles are equal

Front 18

ABCDE ↔ PONMQ

Back 18

arrow shows correspondence of vertices

Front 19

Corollary to the definition of congruent triangles

Back 19

Two triangles congruent to a third triangle are congruent to each other

Front 20

Included side

Back 20

side AB included by A and B, opposite of C

Front 21

included angle

Back 21

angle is included by sides forming that vertex, opposite to third side of triangle

Front 22

Postulate 5. ASA Postulate

Back 22

If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent

Front 23

Postulate 6. SAS Postulate

Back 23

If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent

Front 24

Brief Restatement of congruence definition

Back 24

Corresponding parts of congruent triangles are equal

Front 25

definition scalene

Back 25

a triangle is scalene iff it has no equal sides

Front 26

definition isosceles

Back 26

a triangle is isosceles iff it has at least 2 equal sides

Front 27

definition equilateral

Back 27

a triangle is equilateral iff all of its sides are equal

Front 28

definition obtuse

Back 28

a triangle is obtuse iff it has an obtuse angle

Front 29

definition right

Back 29

a triangle is right iff it has a right angle

Front 30

definition acute

Back 30

a triangle is acute iff ALL of its angles are acute

Front 31

definition equiangular

Back 31

a triangle is equiangular iff all of its angles are equal

Front 32

Theorem 9

Back 32

If two sides of a triangle are equal, the angles opposite them are equal

Front 33

Theorem 10

Back 33

If two angles of a triangle are equal, the sides opposite them are equal

Front 34

Corollaries to Theorems 9 and 10

Back 34

An equilateral triangle is equiangular.
An equiangular triangle is equilateral.

Front 35

Theorem 11. The SSS Theorem

Back 35

If the three sides of one triangle are equal to the three sides of another triangle, the triangles are congruent

Front 36

Construction 3. to copy a line segment

Back 36

set radius of compass to length of AB

Front 37

Construction 4. to copy an angle

Back 37

draw segment for new, draw arc on old and new, set radius to old, mark on new

Front 38

Construction 5. to copy a triangle

Back 38

copy segment
use compass to find opposite vertex