Geometry Conjectures

Front 1

Perpendicular Bisector Conjecture

Back 1

If a point is on the perpendicular bisector of a segment, then it is equally distant fromt he endpoints.

Front 2

Converse of the Perpendicular Bisector Conjecture

Back 2

If a point is equally distant from the endpoints of a segment, then it is on the perpendicualr bisector of the segment.

Front 3

Shortest Distance Conjecture

Back 3

The shortest distance from a point to a line is measured along the perpendicular from the point to the line.

Front 4

Angle Bisector Conjecture

Back 4

If a point is on the bisector of an angle, then it is equally distant from the sides of the angle.

Front 5

Sum of each angle in an equilateral triangle.

Back 5

60 degrees

Front 6

The three angle bisectors of a triangle are ?

Back 6

concurrent

Front 7

The three perpendicualr bisectors of a triangle are?

Back 7

concurrent

Front 8

The three altitudes (or the lines through the altitudes) of a triangle are?

Back 8

concurrent

Front 9

The circumcenter of a triangle is ________distant from the triangle's three vertices.

Back 9

equally

Front 10

The incenter of a triangle is ________distant from the triangle's three sides.

Back 10

equally

Front 11

The three medians of a triangle are ?

Back 11

concurrent

Front 12

The centroid of a triangle divides divides each median into _________ parts so that the distance from the centroid to the vertex is ______ the distance from the centroid ot the midpoint.

Back 12

two parts
twice

Front 13

The circumcenter, centroid, and the orthocenter are three points of concurrency that lie on the _______?

Back 13

Euler line

Front 14

The centroid divides the Euler segment into _______so that the smaller part is _____as long as the longer part.

Back 14

two parts
half

Front 15

Verical Angles Conjecture

Back 15

If two angles are vertical angles, then they are congruent.

Front 16

Linear Pair Conjecture

Back 16

If two angles are a linear pair, then they are supplementary.

Front 17

Parallel Lines Conjecture

Back 17

If two parallel lines are cut by a transversal, then corresponding angles are congruent, alternate interior angles are congurent, and alternate exterior angles are congruent.

Front 18

Corresponding Angle Conjecture (CA Conjecture)

Back 18

If two parallel lines are cut by a transversal, then corresponding angles are congurent.

Front 19

Alternate Interior Angle Conjecture (AIA Conjecture)

Back 19

If two parallel lines are cut by a transversal then alternate interior angles are congurent.

Front 20

Alternate Exterior Angle Conjecture (AEA Conjecture)

Back 20

If two parallel lines are cut by a transverasl, then alternate exterior angles are congruent.

Front 21

Converse of the Parallel Lines Conjecture

Back 21

If two lines are cut by a transversal to form pairs of congruent corresponding angles, congruent alternate interior angles, and congruent alternate exterior angles, then the lines are parallel.

Front 22

Coordinate Midpoint Conjecture

Back 22

If (x1x2) and (y1y2) are the coordinates of the endpoints of a segment, the the coordinates of the midpoint are (x1+x2,y1+y2/2)

Front 23

Slope Line Conjecture

Back 23

The slope m of a line (or segment) through P1 and P2 with coordinates (x1,y1) and (x2,y2) where (x1 does not equal x2) is m = y2-y1/x2-x1.

Front 24

Parallel Slope Conjecture

Back 24

In a coordinate plane, two distinct lines are parallel if an only if their slopes are equal.

Front 25

Perpendicular Slope Conjecture

Back 25

In a coordinate plane, two nonvertical lines are perpendicular if and only if their slopes are the negative reciprocals of each other.

Front 26

Slope-Intercept Conjecture

Back 26

If the graph of a line has a slope of m and a y-intercept of (0,b), the the equation of the line can be written in the form y=mx+b.

Front 27

Centroid Coordinates Conjecture

Back 27

If triangle TRY has coordinates T(a,d), R(b,e),and Y (c,f then the centroid has coordinates (a+b+c/3, d+e+f/3)

Front 28

Triangle Sum Conjecture

Back 28

The sum of the measures of the angles in a triangle is 180 degrees.

Front 29

Third Angle Conjecture

Back 29

If two angles of one triangle are equal in measure to two angles of another triangle, then the third angle in each triangle is equal in measure to the third angel in the other triangle.

Front 30

Isosceles Triangle Conjecture

Back 30

If a triangle is isosceles, then its base angles are congruent.

Front 31

Converse of the Isocsceles Triangle Conjecture

Back 31

If a triangle has two congruent angles, then it is an isosceles triangle.

Front 32

Equilateral Triangle Conjecture

Back 32

An equilateral triangle is equiangular, and, conversely, an equiangular triangle is equilateral.

Front 33

Triangle Inequality Conjecture

Back 33

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Front 34

Side-Angle Inequality Conjecture

Back 34

In a triangle, the longest side is opposite the angle with greatest measure and the shortest side is opposite the angle with least measure.

Front 35

Triangle Exterior Angle Conjecture

Back 35

The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

Front 36

SSS Congruence Conjecture

Back 36

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

Front 37

SAS Congruence Conjecture

Back 37

If two sides and the angle between them in one triangle are congruent to two sides and the angle between them in another triangle, then the triangles are congruent.

Front 38

Conjecture regarding 2 sides and an angle not between the two sides

Back 38

If two sides and an angle that is not between the two sides in one triangle are congruent to the corresponding two sides and an angle that is not between the two sides in another triangle, then the two triangles are not necessarily congruent.

Front 39

ASA Congruence Conjecture

Back 39

If two angles and the side between them in one triangle are congruent to two angles and the side between them in another triangle, then the triangles are congruent.

Front 40

SAA Congruence Conjecture

Back 40

If two angles and a side that is not between them in one triangle are congruent to the corrresponding two angles and side not between them in another triangle,then the triangles are congruent.

Front 41

Conjecture regarding 3 angles of a triangle

Back 41

If the three angles of one triangle are congruent to the three angles of another triangle, then the two triangles are not necessarily congruent.

Front 42

Vertex Angle Bisector Conjecture

Back 42

In an isosceles triangle, the bisector of the vertex angle is also the altitude to the base and the median to the base.

Front 43

Quadrilateral Sum Conjecture

Back 43

The sum of the measures of the four angles of every quadrilateral is 360 degrees.

Front 44

Polygon Sum Conjecture

Back 44

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

Front 45

Exterior Angle Sum Conjecture

Back 45

The sum of the measures of one set of exterior angles is 360 degrees.