Geometry: FAQ

When two lines intersect, they form angles with each other. Different types of angles have different relationships to one another. For example, vertical angles always have equal measures, while supplementary angles have measures that add up to $180$‍ degrees.

Parallel lines are lines that never intersect. A transversal is a line that crosses two or more lines, and it can create interesting relationships between the angles formed.

The sum of the measures of the three interior angles in a triangle is always $180$‍ degrees. So, if we know two of the angle measures, we can use that information to find the measure of the third angle.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two other sides. It's often written as the equation $a^2+b^2=c^2$‍.

We can draw a right triangle between the two points, and then use the Pythagorean theorem to find the hypotenuse, which is the distance we're looking for.

Volume is a measure of the amount of space an object takes up. It's important for both practical and theoretical reasons. For example, if we're building a container to hold a certain amount of liquid, we need to know how to calculate the volume so we can make sure the container is big enough.

Many of the topics in this unit have a wide range of applications. For example, the Pythagorean theorem is used in fields like architecture, construction, and surveying. Understanding angles is important for everything from drafting to robotics. And knowing how to calculate volume is crucial in a number of industries, from manufacturing to food and beverage.