What are geometry conjectures?

In mathematics, a conjecture is a conclusion or a proposition which is suspected to be true due to preliminary supporting evidence, but for which no proof or disproof has yet been found.

What conjectures can you make about a point on the perpendicular bisector of a segment and a point on the bisector of an angle?

In a plane, if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. If a point lies on the bisector of an angle, then it is equidistant from the two sides of the angle.

How do conjectures and counterexamples play a role in the process of finding a pattern?

A conjecture is an “educated guess” that is based on examples in a pattern. A counterexample is an example that disproves a conjecture. Suppose you were given a mathematical pattern like h = \begin{align*}-16/t^2\end{align*}. What if you wanted to make an educated guess, or conjecture, about h?

What are the types of conjectures?

Parallel Lines Conjectures: Corresponding, alternate interior, and alternate exterior angles. Parallelogram Conjectures: Side, angle, and diagonal relationships. Rhombus Conjectures: Side, angle, and diagonal relationships. Rectangle Conjectures: Side, angle, and diagonal relationships.

How do you test conjectures?

TESTING CONJECTURES. The first question that we face in evaluating a conjecture is gauging whether it is true or not. While confirming examples may help to provide insight into why a conjecture is true, we must also actively search for counterexamples.

Who proved the Poincare conjecture?

In 1961 Stephen Smale shocked mathematicians by proving the Generalized Poincaré conjecture for dimensions greater than four and extended his techniques to prove the fundamental h-cobordism theorem. In 1982 Michael Freedman proved the Poincaré conjecture in four dimensions.

How do you prove conjectures?

The most common method for proving conjectures is direct proof. This method will be used to prove the lattice problem above. Prove that the number of segments connecting an n × n n\times n n×n lattice is 2 n ( n + 1 ) 2n(n+1) 2n(n+1). Recall from the previous example how the segments in the lattice were counted.