What is the conjecture about parallel lines?

The Alternate Interior Angle Conjecture states: “If two parallel lines are intersected by a transversal, then alternate interior angles are congruent.”

Which conjectures are for patterns using parallel lines?

Conjecture (Alternate Interior Angles Conjecture ): If two parallel lines are cut by a transversal, the alternate interior angles are congruent. Conjecture (Alternate Exterior Angles Conjecture ): If two parallel lines are cut by a transversal, the corresponding angles are congruent.

What conjectures can you make about the sides angles and diagonals of a parallelogram?

That is, not only are the opposite sides parallel, they are also congruent; opposite angles are congruent; and the diagonals of a parallelogram bisect each other.

What is the AIA conjecture in math?

Alternate Interior Angles Conjecture, or AIA Conjecture: If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

What are the geometry conjectures?

Vertical Angle Conjecture: Non-adjacent angles formed by two intersecting lines. Linear Pair Conjecture: Adjacent angles formed by two intersecting lines. Triangle Sum Conjecture: Sum of the measures of the three angles in a triangle. Quadrilateral Sum Conjecture: Sum of the four angles in a convex four-sided figure.

What is a conjecture in geometry?

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 = − 16 / t 2 .

What conjectures can you make about perpendicular lines?

If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line. In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

How do you construct a conjecture in a parallelogram?

Conjecture (Parallelogram Conjecture II ): Adjacent angles in a parallelogram are supplementary. Conjecture (Parallelogram Conjecture III ): Opposite sides of a parallelogram are equal in length. Conjecture (Parallelogram Conjecture IV ): The diagonals of a parallelogram are bisected by the point of their intersection.

How do you prove the converse of the AIA theorem?

If two lines are cut by a transversal so that the corresponding angles are congruent, then the lines are parallel. Theorem 3.8: Alternate Interior Angles Converse: If two lines are cut by a transversal so that the alternate interior angles are congruent, then the lines are parallel.

What is a conjecture give an example?

A conjecture is a good guess or an idea about a pattern. For example, make a conjecture about the next number in the pattern 2,6,11,15… The terms increase by 4, then 5, and then 6. Conjecture: the next term will increase by 7, so it will be 17+7=24.

What is conjecture give example?

A statement that might be true (based on some research or reasoning), but is not proven. Like a hypothesis, but not stated in as formal, or testable, way. So a conjecture is like an educated guess. Example: I heard the sound of a plastic bag, so I conjecture there might be some food!

What is the difference between theorem and converse?

In math, when you have a theorem, you likely have a converse theorem. Do you know what converse means? The converse of a theorem happens when the conclusion and hypothesis of a theorem are switched.

What is theorem 3.8 in geometry?

Theorem 3.8: If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.

What are conjectures in geometry?

A conjecture is an educated guess that is based on known information. Example. If we are given information about the quantity and formation of section 1, 2 and 3 of stars our conjecture would be as follows.

How do you solve a conjecture?

Disproving a conjecture may be simpler than actually proving it to be true. All you need to disprove a conjecture is one example. That example is called a counterexample. Remember that ‘counter’ means to go against, so a counterexample is a statement used to disprove a conjecture.