Geometry Semester 1 Final Review

Front

What is the distance formula in geometry?

Back

The distance formula is used to determine the distance between two points (x1, y1) and (x2, y2) in a coordinate plane: \(d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\).

Front

What is a counterexample?

Back

A counterexample is an example that disproves a statement or proposition. For instance, the number 42 is a counterexample to the statement 'All numbers that are divisible by 2 are divisible by 4.'

Front

How do you calculate the surface area of a square pyramid?

Back

The surface area of a square pyramid is calculated using the formula: \(SA = B + \frac{1}{2}Pl\), where B is the area of the base, P is the perimeter of the base, and l is the slant height.

Front

What happens to the coordinates of a point when it is reflected over the y-axis?

Back

When a point (x, y) is reflected over the y-axis, its new coordinates become (-x, y). For example, the point (-5, 2) becomes (5, 2).

Front

What is a conditional statement in logic?

Back

A conditional statement is an if-then statement that expresses a relationship between two propositions. For example, 'If it rains, then the ground will be wet.'

Front

What is the contrapositive of a conditional statement?

Back

The contrapositive of a conditional statement 'If P, then Q' is 'If not Q, then not P.' It is logically equivalent to the original statement.

Front

What is the formula for the area of a triangle?

Back

The area of a triangle is calculated using the formula: \(A = \frac{1}{2}bh\), where b is the base and h is the height.

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): \(c^2 = a^2 + b^2\).

Front

What is the definition of a polygon?

Back

A polygon is a closed figure formed by a finite number of straight line segments connected end to end. Examples include triangles, quadrilaterals, and pentagons.

Front

What is the difference between a radius and a diameter of a circle?

Back

The radius of a circle is the distance from the center to any point on the circle, while the diameter is the distance across the circle through the center, equal to twice the radius.