## 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.