Triangle Totals worksheet: Use addition facts to make each side of the triangle add up to 20.

The image shows a math worksheet titled "Triangle Totals", which focuses on addition facts to 20. The task is to fill in the circles at the corners of each triangle so that the sum of the numbers on each side equals 20.

---

🔍 Problem Breakdown:

Each triangle has:
- Three corners (circles) where you place numbers.
- Three sides, each consisting of two corner numbers (one at each end).
- The sum of the two numbers on each side must be 20.

For example, in the solved triangle on the right:

```
5
/ \
5 8
/ \
10 7
```

Let’s verify the sides:
- Top side: 5 + 5 = 10 ✘ → Wait! That doesn’t add to 20.

Wait — this seems incorrect. Let's double-check.

Actually, looking closely:

- Top side: 5 (top) and 5 (bottom-left)? No — the layout suggests:
- Top vertex: 5
- Bottom-left vertex: 10
- Bottom-right vertex: 7

So the three sides are:
1. Top to bottom-left: 5 + 10 = 15
2. Top to bottom-right: 5 + 7 = 12
3. Bottom-left to bottom-right: 10 + 7 = 17

That’s not adding to 20. But wait — there's a number in the center labeled 20.

Ah! So the center number is the total for each side. That means:
- Each side (edge) must have two numbers (at the ends) that add up to 20.
- The center number (20) is the target sum.

But in the diagram, it looks like the numbers on the vertices are:
- Top: 5
- Bottom-left: 10
- Bottom-right: 7

Then the edges are:
- Left edge: 5 (top) + 10 (bottom-left) = 15 ≠ 20
- Right edge: 5 (top) + 7 (bottom-right) = 12 ≠ 20
- Base: 10 + 7 = 17 ≠ 20

This does not work.

Wait — perhaps I'm misinterpreting the layout.

Let me re-express the given solved example correctly:

Looking at the right-hand side of the image:

```
5
/ \
5 8
/ \
10 7
```

With 20 written in the middle.

Now let's label the positions:
- Top circle: 5
- Left bottom: 10
- Right bottom: 7
- Then there's a middle number on each side?

Wait — no, the 5, 8, 3 are on the edges, not the vertices.

Let’s look again.

Actually, the correct interpretation is:

Each side of the triangle has three circles:
- Two at the vertices
- One in the middle of the side

And the total of the three numbers on each side must equal 20?

No — the instruction says:
> "Can you use your addition fact skills to make sure that each side adds up to 20?"

And the first one is done for you.

Looking carefully:

In the first triangle (on the right):

- Top vertex: 5
- Middle of left side: 5
- Bottom-left vertex: 10
- Middle of right side: 8
- Bottom-right vertex: 7
- Middle of base: 3

Wait — that’s six numbers.

But the triangle only has three sides, and each side has three circles? That would be 6 circles total (3 vertices, 3 midpoints).

But the diagram shows:
- Top: 5
- Left side: 5 (middle)
- Bottom-left: 10
- Right side: 8 (middle)
- Bottom-right: 7
- Base: 3 (middle)

So the sides are:
1. Left side: 5 (top) + 5 (middle-left) + 10 (bottom-left) = 20 ✔
2. Right side: 5 (top) + 8 (middle-right) + 7 (bottom-right) = 20 ✔
3. Base: 10 (bottom-left) + 3 (middle-base) + 7 (bottom-right) = 20 ✔

Yes! So now it makes sense.

✔ Correct Interpretation:

Each side of the triangle has three numbers:
- One at each vertex
- One in the middle of the side

And the sum of the three numbers on each side must be 20.

The center number (20) is just labeling the goal.

So the problem is:
> Fill in the empty circles so that the sum of the three numbers on each side equals 20.

---

🧩 How to Solve It

We need to find values for the empty circles such that:
- Each side sums to 20.
- Numbers are likely whole numbers (possibly from 1–9 or 1–10), based on typical grade-level problems.

Let’s analyze the first completed example:

```
5
/ \
5 8
/ \
10 7
\ /
3 ?
\ /
?
```

Wait — actually, the base has:
- Left: 10
- Middle: 3
- Right: 7
→ 10 + 3 + 7 = 20 ✔

Left side: 5 (top) + 5 (left-middle) + 10 (bottom-left) = 20 ✔

Right side: 5 (top) + 8 (right-middle) + 7 (bottom-right) = 20 ✔

So all sides sum to 20.

Now, the task is to create other triangles where the sum of each side is 20, using different combinations.

---

🔁 Strategy to Find Different Solutions

We can try to create new configurations by choosing numbers for the vertices and then solving for the midpoint numbers.

Let’s define:
- A = top vertex
- B = bottom-left vertex
- C = bottom-right vertex
- D = midpoint of left side (between A and B)
- E = midpoint of right side (between A and C)
- F = midpoint of base (between B and C)

Then:
- Side 1 (left): A + D + B = 20
- Side 2 (right): A + E + C = 20
- Side 3 (base): B + F + C = 20

We can pick values for A, B, C, then solve for D, E, F.

But we must ensure all numbers are reasonable (e.g., positive integers, maybe ≤ 10 or 15).

Let’s try an example.

---

✔ Example Solution 1 (New Configuration)

Let’s pick:
- A = 6 (top)
- B = 8 (bottom-left)
- C = 9 (bottom-right)

Then:
- Left side: 6 + D + 8 = 20 → D = 6
- Right side: 6 + E + 9 = 20 → E = 5
- Base: 8 + F + 9 = 20 → F = 3

So the triangle is:

```
6
/ \
6 5
/ \
8 9
\ /
3 ?
\ /
?
```

Wait — the base should have F = 3 in the middle.

So:

```
6
/ \
6 5
/ \
8 9
\ /
3 ?
\ /
?
```

Actually, the base is 8 + 3 + 9 = 20 ✔

All sides sum to 20.

So this is a valid solution.

---

✔ Example Solution 2

Try:
- A = 4
- B = 10
- C = 10

Then:
- Left: 4 + D + 10 = 20 → D = 6
- Right: 4 + E + 10 = 20 → E = 6
- Base: 10 + F + 10 = 20 → F = 0

F = 0 — might be acceptable if allowed, but maybe avoid zero.

Try:
- A = 7
- B = 6
- C = 8

Then:
- Left: 7 + D + 6 = 20 → D = 7
- Right: 7 + E + 8 = 20 → E = 5
- Base: 6 + F + 8 = 20 → F = 6

So:

```
7
/ \
7 5
/ \
6 8
\ /
6 ?
\ /
?
```

Base: 6 + 6 + 8 = 20 ✔

All good.

---

✔ General Tips

To find different ways to make a total of 20:
1. Choose any three numbers for the vertices (A, B, C).
2. Calculate the midpoint numbers:
- D = 20 - A - B
- E = 20 - A - C
- F = 20 - B - C
3. Make sure D, E, F are positive integers (or within range).
4. Avoid duplicates if trying to find distinct configurations.

---

✔ Answer Summary

You can create multiple valid triangles by choosing different vertex numbers and calculating the required midpoints.

Example solutions:

1. Vertices: 6, 8, 9 → Midpoints: 6, 5, 3
2. Vertices: 7, 6, 8 → Midpoints: 7, 5, 6
3. Vertices: 5, 10, 7 → Midpoints: 5, 8, 3 (the given one)

You can continue exploring!

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📝 Final Answer:

Yes, you can find multiple ways to make each side total 20 by choosing different numbers for the vertices and computing the required midpoints. For example:

- Use vertices: 6, 8, 9 → midpoints: 6, 5, 3
- Use vertices: 7, 6, 8 → midpoints: 7, 5, 6
- Use vertices: 4, 12, 4 → midpoints: 4, 4, 4 (if larger numbers allowed)

Just ensure that the sum of the three numbers on each side equals 20.

✔ This activity helps reinforce addition facts and problem-solving with constraints.