Printable primary math worksheet for math grades 1 to 6 based on ... - Free Printable

The task in the image is to draw the height (also known as the altitude) for each triangle, using the side labeled "base" as the reference.

---

🔷 What is the Height of a Triangle?

The height (or altitude) of a triangle relative to a given base is the perpendicular distance from the opposite vertex to the line containing the base.

> ✔ Key Rule: The height must be perpendicular (at a 90° angle) to the base and extend from the opposite vertex.

---

🧩 How to Draw the Height:

For each triangle:
1. Identify the side labeled "base".
2. Find the vertex opposite to that base (the one not on the base).
3. From that vertex, draw a line perpendicular to the base.
- If the triangle is acute or right, the height will fall inside the triangle.
- If the triangle is obtuse, the height may fall outside the triangle — you may need to extend the base to draw the perpendicular.

---

✔ Step-by-Step Solution for Each Triangle

Let’s go through each triangle in the grid (left to right, top to bottom):

#### 🔹 1st Triangle (Top-left)
- Base is the bottom horizontal side.
- Opposite vertex is at the top.
- Draw a perpendicular line from the top vertex down to the base.
- Since it's an acute triangle, the height lies inside.

#### 🔹 2nd Triangle (Top-middle)
- Base is the bottom side.
- Opposite vertex is at the top.
- Draw a perpendicular from the top vertex to the base.
- This is an acute triangle, so height is inside.

#### 🔹 3rd Triangle (Top-right)
- Base is the bottom side.
- Opposite vertex is at the top-left.
- Draw a perpendicular from that vertex to the base.
- This is an obtuse triangle, so the height might fall outside — extend the base if needed.

#### 🔹 4th Triangle (Middle-left)
- Base is the bottom-left slanted side.
- Opposite vertex is at the top.
- Draw a perpendicular from the top vertex to the base.
- The height may lie outside since this is likely obtuse.

#### 🔹 5th Triangle (Center)
- Base is the bottom side.
- It’s an equilateral or isosceles triangle.
- Draw a perpendicular from the top vertex straight down to the midpoint of the base.
- This height falls inside.

#### 🔹 6th Triangle (Middle-right)
- Base is the bottom side.
- Opposite vertex is at the top-left.
- Draw a perpendicular from that vertex to the base.
- Again, possibly obtuse — height may fall outside.

#### 🔹 7th Triangle (Bottom-left)
- Base is the bottom side.
- Opposite vertex is at the top-right.
- Draw a perpendicular from the top vertex to the base.
- Likely acute or right — height inside.

#### 🔹 8th Triangle (Bottom-middle)
- Base is the bottom side.
- Opposite vertex is at the top-left.
- Draw a perpendicular from that vertex to the base.
- Height should fall inside.

#### 🔹 9th Triangle (Bottom-right)
- Base is the bottom side.
- Opposite vertex is at the top.
- Draw a perpendicular from the top vertex to the base.
- This looks like a right triangle — the height may coincide with one leg.

---

✏️ Summary of How to Draw Each Height:

| Triangle | Base | Action |
|--------|------|--------|
| 1 | Bottom | Draw perpendicular from top vertex to base (inside) |
| 2 | Bottom | Draw perpendicular from top vertex (inside) |
| 3 | Bottom | Draw perpendicular from top-left vertex (may extend base) |
| 4 | Left-slanted | Draw perpendicular from top vertex to base (may be outside) |
| 5 | Bottom | Draw perpendicular from top to center of base (inside) |
| 6 | Bottom | Draw perpendicular from top-left vertex (likely outside) |
| 7 | Bottom | Draw perpendicular from top-right vertex (inside) |
| 8 | Bottom | Draw perpendicular from top-left vertex (inside) |
| 9 | Bottom | Draw perpendicular from top vertex (inside or along leg) |

---

📝 Final Instructions (for student):

For each triangle:
1. Use a ruler and protractor or set square to ensure the line is perpendicular.
2. Label the height with a small right-angle symbol (└) where it meets the base.
3. Optionally, label the height as “h”.

---

🎯 Example (Visual Guide – Text Description)

For Triangle 1:
```
/|
/ |
/ |
/ | h
/____|_____
base
```

The vertical line `h` from the top vertex down to the base is the height.

---

✔ All heights are drawn by dropping a perpendicular from the opposite vertex to the line of the base.

Would you like me to generate a visual version of the completed worksheet? I can describe how to draw each height in detail or provide instructions for a digital drawing tool.