Lesson 18: Lines and Angles

New Concept

An angle is two rays with the same endpoint. Angles are commonly described by their measure:

• Acute: Between $0^\circ$ and $90^\circ$
• Right: $90^\circ$
• Obtuse: Between $90^\circ$ and $180^\circ$
• Straight: $180^\circ$

What’s next

Soon, you'll use these definitions to practice naming geometric figures, classifying different types of angles, and solving problems about their measures.

Property

A line ($\overleftrightarrow{AB}$) is a straight path that extends forever in both directions. A ray ($\overrightarrow{AB}$) is part of a line with one starting point and extends forever in one direction. A segment ($\overline{AB}$) is part of a line with two endpoints.

Examples

• A line passing through points X and Y is named $\overleftrightarrow{XY}$ or $\overleftrightarrow{YX}$.
• A ray starting at endpoint P and passing through Q is named $\overrightarrow{PQ}$.
• A segment with endpoints M and N is named $\overline{MN}$ or $\overline{NM}$.

Explanation

Think of a line as an endless highway. A ray is like a flashlight beam; it starts from the bulb and goes on forever in one direction, so order matters when naming it! A segment is just a small piece of that highway, like the distance between two specific exits. It has a clear beginning and end.

Property

Parallel lines are lines on the same plane that never intersect. Perpendicular lines are lines that intersect to form right angles ($90^\circ$). Skew lines are lines on different planes that do not intersect.

Examples

• The two rails of a straight railroad track are an example of parallel lines.
• The intersection of a window's horizontal and vertical frames forms perpendicular lines.
• An overpass crossing a highway represents skew lines, as they are on different planes and do not intersect.

Explanation

Imagine train tracks—they are parallel, always the same distance apart. The corner of a room where the floor meets a wall is perpendicular, forming a perfect square corner. Skew lines are trickier; think of an airplane's flight path and a highway below. They are not parallel and will never, ever cross paths!

Property

Angles are classified by their measure in degrees. An acute angle is between $0^\circ$ and $90^\circ$. A right angle is exactly $90^\circ$. An obtuse angle is between $90^\circ$ and $180^\circ$. A straight angle is exactly $180^\circ$.

Examples

• A single slice of a standard pizza typically has an acute angle at its tip.
• The four corners of a square piece of paper are all perfect right angles.
• A handheld fan opened wide creates an obtuse angle between its blades.

Explanation

Think of opening a book! When you just crack it open, the angle is acute (it's a cute little angle). Open it to a perfect 'L' shape, and that's a right angle. When it's opened wide, it becomes obtuse. Lay the book completely flat, and you have a straight angle, forming a perfect line.