Hello! Welcome to the world of "Perpendicular and Parallel" lines
You often draw "lines" in math class, don't you? But have you ever paid attention to the "relationship" between how two lines are arranged?
In this chapter, we will learn about "perpendicular" and "parallel", which are super important concepts for understanding shapes. Once you know these, you'll start to see the shapes of buildings and road designs around you in a whole new way!
At first, you might feel like "using two set squares is tricky..." but don't worry. Once you get the hang of it, anyone can draw them neatly. Let's have fun learning together!
1. What is "perpendicular"?
When two lines intersect and the angle formed is a right angle (90 degrees), the two lines are said to be perpendicular to each other.
How to find perpendicular lines
If you're wondering, "Is this perpendicular?", try placing the right-angle corner of your set square against the intersection. If it fits perfectly, it's perpendicular!
Common examples of "perpendicular"
- Vertical and horizontal lines on grid paper
- The corners of a classroom door
- A crossroads (four-way intersection)
【Fun Fact】 The secret of the kanji for "perpendicular" (垂直)
The character "垂" (sui) implies "hanging straight down." If you hang a string with a weight on it, it points straight down toward the ground, which is perpendicular to the earth. People in the past measured "straight 90-degree angles" this way.
Pro-tip: Even if two lines aren't touching, if they form a right angle when you extend them, those two lines are considered perpendicular!
Summary: If two lines cross at a 90-degree (right) angle, they are "perpendicular"!
2. What is "parallel"?
When two straight lines are perpendicular to the same line, the two lines are said to be parallel to each other.
In simpler terms, it refers to "two lines that will never meet, no matter how far you extend them."
Characteristics of parallel lines
- No matter how long you extend them, the two lines will never overlap.
- The width (distance) between the two lines is the same everywhere.
- When a third line intersects them diagonally, the angles formed at the intersections are equal.
Common examples of "parallel"
- Train tracks (it would be a disaster if they touched!)
- The side bars of a ladder
- The horizontal lines on your notebook
Common mistake: You might think, "They don't look like they cross, so they must be parallel!" But even if they are tilted just a tiny bit, they might cross far off in the distance. It is important to check if the width is the same everywhere.
Summary: If they maintain the same width and never ever cross, they are "parallel"!
3. Let's draw them neatly using set squares!
When drawing perpendicular or parallel lines, we use a pair of set squares as a team. Let's pretend we're professional architects!
How to draw perpendicular lines
1. Align one set square with the reference line.
2. Place the right-angle corner of the second set square against the edge of the first one.
3. Draw the line along the edge of the second set square, and you're done!
How to draw parallel lines
1. Align one set square with the reference line.
2. Place the second set square firmly against the first to act as a "rail."
3. Slide the first set square along the rail.
4. Draw a line wherever you like, and you've drawn a parallel line!
Tip: The secret to success is using your left hand to hold the "rail" set square firmly so it doesn't move.
4. Quadrilaterals using parallel and perpendicular lines
Using the "perpendicular" and "parallel" concepts we've learned, let's categorize some special quadrilaterals.
Trapezoid
A quadrilateral with at least one pair of sides that are parallel. (Example: The side profile of a playground slide)
Parallelogram
A quadrilateral where both pairs of opposite sides are parallel.
Characteristics: Opposite sides are equal in length, and opposite angles are equal in size.
Rhombus
A quadrilateral where all four sides are the same length.
Characteristics: Opposite sides are parallel. Also, the diagonals intersect at a perpendicular angle!
Point: Squares and rectangles are actually members of the parallelogram family, too. It's fun to look for hidden perpendicular or parallel lines in them!
Lastly: If you get stuck...
Perpendicular and parallel lines are the absolute basics of geometry. If you feel they are difficult, try grabbing a ruler and finding lots of "right angles (perpendicular)" and "parallel lines" around your house.
The more you discover "Oh, there's one too!", the better you will become at math.
Don't rush; take it one step at a time at your own pace. I'm rooting for you!