Discovering Geometry - Conjectures

conjecture

A conclusion you reach using inductive reasoning.

Triangle Midsegment Conjecture

A midsegment of a triangle is parallel to the third side and half the length of the third side

Equilateral/Equiangular Triangle Conjecture

All sides/angles have equal measurements. Bioconditional conjecture

Exterior Angle Sum Conjecture

For any polygon, the sum of the measures of a set of exterior angles is 360.

Converse Perpendicular Bisector Conjecture

If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.

Angle Bisector Conjecture

If a point is on the bisector of an angle, then it is equidistant from the sides of the angle

Converse Isosceles Triangle Conjecture

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

Isosceles Triangle Conjecture

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

Side-Side-Side (SSS) Congruency Conjecture

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

Side-Angle-Angle (SAA) Congruency Conjecture

If two angles and a non included side of one triangle are congruent to the corresponding angles and side of another triangle, then the triangles are congruent

Angle-Side-Angle (ASA) Congruency Conjecture

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

Vertical Angles Conjecture

If two angles are vertical angles, then they're congruent

Linear Pair Conjecture

If two angles form a linear pair then the measures of the angles add up to 180°.

Converse of the Parallel Lines Conjecture

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

Alternate Exterior Angle Conjecture (AEA Conjecture)

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

Alternate Interior Angles Conjecture (AIA Conjecture)

If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.

Double-Edged Straightedge Conjecture

If two parallel lines are intersected by a second pair of parallel lines that are the same distance apart as the first pair, then the parallelogram formed is a rhombus.

Side-Angle-Side (SAS) Congruency Conjecture

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

Side-Angle Inequality Conjecture

In a triangle, if one side is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.

Centroid Conjecture

The centroid of a triangle divides each median into two parts so that the distance from the centroid to the vertex is twice the distance from the centroid to the midpoint of the opposite side

Center of Gravity Conjecture

The centroid of a triangle is the center of gravity of the triangular region. You can balance a triangle on its centroid

Circumcenter Conjecture

The circumcenter of a triangle is equidistant from the three vertices.

Trapezoid Consecutive Angles Conjecture

The consecutive angles between the bases of a trapezoid are supplementary (equal 180 when added together)

Kite Diagonals Bisector Conjecture

The diagonal connecting the vertex angles of a kite is the perpendicular bisector of the other diagonal.

Kite Diagonals Conjecture

The diagonals of a kite are perpendicular

Parallelogram Diagonals Conjecture

The diagonals of a parallelogram bisect each other.

Rectangle Diagonals Conjecture

The diagonals of a rectangle are congruent and bisect each other

Rhombus Angles Conjecture

The diagonals of a rhombus bisect the angles of the rhombus.

Incenter Conjecture

The incenter of a triangle is equidistant from the three sides

Trapezoid Midsegment Conjecture

The midsegment of a trapezoid is parallel to the bases, and it's half the sum of the lengths of the bases

Kite Angles Conjecture

The non-vertex angles of a kite are congruent

Parallelogram Opposite Angles Conjecture

The opposite sides of a parallelogram are congruent.

Parallelogram Opposite Sides Conjecture

The opposite sides of a parallelogram are congruent.

Shortest Distance Conjecture

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

Triangle Inequality Conjecture

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

Triangle Sum Conjecture

The sum of the measures of the angles in every triangle is 180°.

Pentagon Sum Conjecture

The sum of the measures of the five angles of any pentagon is 540 degrees

Quadrilateral Sum Conjecture

The sum of the measures of the four angles of any quadrilateral is 360°.

Polygon Sum Conjecture

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

Altitude Concurrency Conjecture

The three altitudes (or the lines containing the altitudes of a triangle meet at the orthocenter, which can be outside the triangle

Angle Bisector Concurrency Conjecture

The three angle bisectors of a triangle meet at a point.

Median Concurrency Conjecture

The three medians of a triangle are concurrent (meet at one point)

Three Midsegments Conjecture

The three midsegments of a triangle divide it into four congruent triangles.

Equiangular Polygon Conjecture

You can find the measure of each interior angle of an equiangular n-gon by using the formula 180(n-2)/n.

bioconditional conjectures

a conjecture in which one condition cannot be true unless the other condition is also true. "if and only if"

Overlapping Segments Conjecture

a given segment with points A, B, C, D the following statements are true. If AB=CD, then AC=BD. If AC=BD, then AB=CD.

Side-Side-Angle (SSA) Congruency Conjecture

does NOT prove triangles congruent

Perpendicular Bisector Conjecture

if a point is on the perpendicular bisector of a segment, then it is equidistant for the endpoints

Parallel Line Conjecture

if two parallel lines are cut by a transversal, the corresponding angles are congruent, the alternate interior angles are congruent, and the alternate exterior angles are congruent

Corresponding Angles Conjecture (CA Conjecture)

if two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent

Vertex Angle Bisector Conjecture

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

Isosceles Trapezoid Conjecture

the base angles of an isosceles trapezoid are congruent

Parallelogram Consecutive Angles Conjecture

the consecutive angles of a parallelogram are supplementary (equal 180 when added together)

Rhombus Diagonals Conjecture

the diagonals of a rhombus are perpendicular and they bisect each other

Square Diagonals Conjecture

the diagonals of a square are congruent, perpendicular, and bisect each other

Isosceles Trapezoid Diagonals Conjecture

the diagonals of an isosceles trapezoid are congruent

Triangle Exterior Angle Conjecture

the measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles

Perpendicular Bisector Concurrency Conjecture

the three perpendicular bisectors of a triangle are congruent

Kite Angle Bisector Conjecture

the vertex angles of a kite are bisected by a diagonal

converse statement

when you reverse the if - then in a statement