Proof conjecture Perpendicular Bisector Conjecture

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

converseof the perpendicular bisector conjecture

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

shortest distance. Conjecture

States that the shortest distance from a point to a line is the perpendicular distance to that line. Therefore, any point that is equidistant from the segment's endpoints lies on the perpendicular bisector.

Angle bisector conjecture

States that the angle bisector of an angle divides the opposite side into segments that are proportional to the lengths of the other two sides.

angle bisector concurrency conjecture

The angle bisector concurrency conjecture states that the three angle bisectors of a triangle intersect at a single point called the incenter, which is equidistant from all sides of the triangle.

Perpendicular bisector concurrency conjecture

States that the three perpendicular bisectors of a triangle intersect at a single point called the circumcenter, which is equidistant from all vertices of the triangle.

Altitude concurrency conjecture

States that the three altitudes of a triangle intersect at a single point called the orthocenter.

Isosceles triangle conjecture

In an isosceles triangle, the angles opposite the equal sides are also equal.

Converse isosceles triangle conjecture

if two angles in a triangle are congruent, then the sides opposite those angles are also congruent.

Vertical angle conjecture

States that non adjacent angles formed by two intersecting lines are congruent

Linear pair conjecture

States that adjacent angles formed by two intersecting lines are supplementary (add up to 180)

Adjacent lines

two angles that share a common vertex (the point where the lines meet) and a common side (the line segment they both touch), but they do not overlap.

Triangle sum conjecture

States that som of the measures of the three angles add up to 180

Quadrilateral sum conjecture

States that the sum of The measure of the four angles in a convex quadrilateral is 360

Triangle congruency

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Triangle inequality theorem

States that the sim of the lengths of any two sides of a triangle must be greater than the length of third side

Parrelelogram properties

Opposite sides and opposite angles of a parallelogram are congruent. Consecutive angles are supplementary

Special quadrilateral properties rectangle rhombus square

These properties relate to the specific characteristics of each quadrilateral type, such as congruent diagonals, perpendicular diagonals, and bisected diagonals

Parallel line conjecture

corresponding angles formed by parallel lines and a transversal are congruent). 

Corresponding angles

matching sides and angles that occupy the same position in two different shapes.

Tranversal

a line, ray, or line segment that intersects other lines, rays, or line segments at different points on a plane