Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: c² = a² + b².

Front

What is a counterexample?

Back

A counterexample is an example that disproves a conjecture or statement. It shows that the statement is not true in all cases.

Front

What are alternate exterior angles?

Back

Alternate exterior angles are pairs of angles that lie outside two parallel lines and on opposite sides of a transversal. If the lines are parallel, these angles are equal.

Front

How do you find the midpoint of a line segment?

Back

To find the midpoint of a line segment with endpoints (x1, y1) and (x2, y2), use the formula: Midpoint = ((x1 + x2)/2, (y1 + y2)/2).

Front

What does it mean for angles to be supplementary?

Back

Two angles are supplementary if the sum of their measures is 180 degrees.

Front

What is the definition of a transversal?

Back

A transversal is a line that intersects two or more lines at different points. It creates various angles, including corresponding, alternate interior, and alternate exterior angles.

Front

What is the relationship between parallel lines and corresponding angles?

Back

When two parallel lines are cut by a transversal, the corresponding angles are equal.

Front

How do you solve for x in a right triangle?

Back

To solve for x in a right triangle, you can use the Pythagorean theorem or trigonometric ratios (sine, cosine, tangent) depending on the information given.

Front

What is the significance of a conjecture in mathematics?

Back

A conjecture is a statement that is believed to be true based on observations but has not yet been proven. It serves as a starting point for further investigation.

Front

What is the formula for the distance between two points in a coordinate plane?

Back

The distance d between two points (x1, y1) and (x2, y2) is given by the formula: d = √((x2 - x1)² + (y2 - y1)²).