Classify the triangles worksheet for Grade 5 geometry, featuring equilateral, isosceles, scalene, and right triangles.

Let's solve the triangle classification task from the worksheet. The goal is to classify each triangle as equilateral, isosceles, scalene, or right based on its sides and angles.

We’ll go through each triangle one by one, analyzing their side lengths and angles.

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Triangle 1:

- Shape: All three sides appear equal in length.
- Angles: All angles look like they are 60° (since it’s a regular triangle).
- ✔ This is an equilateral triangle.

> Answer: Equilateral

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Triangle 2:

- Shape: One angle looks like a right angle (90°), formed by two perpendicular sides.
- Sides: Two sides appear to be of different lengths; the third side is the hypotenuse.
- ✔ This has a right angle, so it’s a right triangle.
- Also, since all sides appear to be different, it’s scalene.
- But we only need to classify by type — and "right" is a valid classification here.

> Answer: Right

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Triangle 3:

- Shape: Two sides appear to be equal in length (symmetrical).
- Angles: The base angles look equal.
- ✔ This is an isosceles triangle.
- It does not have a right angle, so not a right triangle.

> Answer: Isosceles

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Triangle 4:

- Shape: All three sides appear equal in length.
- Angles: All angles look equal (~60°).
- ✔ This is an equilateral triangle.

> Answer: Equilateral

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Triangle 5:

- Shape: One angle appears to be a right angle (90°).
- Sides: The two legs seem unequal, and the hypotenuse is longer.
- ✔ This is a right triangle.
- Since no sides are equal, it’s also scalene, but again, we classify by the most specific given option.

> Answer: Right

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Triangle 6:

- Shape: One angle is clearly a right angle (90°).
- Sides: Appears to have two equal sides forming the right angle.
- Wait — if two sides are equal and form a right angle, this would be an isosceles right triangle.
- But looking at the image: the two legs are equal, and the hypotenuse is longer.
- ✔ So this is both right and isosceles.
- However, since “right” is a category, and the question asks for classification, we can say:
- It’s a right triangle.
- But note: it’s also isosceles, but unless specified to choose multiple, we pick the most descriptive or primary classification.

But since the instructions say "classify the triangles" and list categories: equilateral / isosceles / scalene / right, we can assume one per triangle.

But some triangles can belong to more than one category.

However, in such worksheets, often you pick the most accurate single classification.

But let’s clarify:

- A triangle can be right and isosceles (e.g., 45-45-90).
- In this case, triangle 6 has a right angle and two equal legs → right isosceles.

But the options listed are:
- equilateral
- isosceles
- scalene
- right

So, if we must pick one, which is best?

But typically, these types are not mutually exclusive. However, the instruction says "classify", implying choose the correct type(s).

But since there's only one blank, likely they expect one answer.

Looking at common practice in such worksheets:
- If a triangle has a right angle, label it right.
- If it has two equal sides, label it isosceles.
- But sometimes they want the most specific.

But here, since the categories are listed separately, perhaps we should pick right if it has a right angle.

Wait — but triangle 2 and 5 are also right triangles.

But triangle 6 is also isosceles.

So maybe the intent is to classify by side length (equilateral, isosceles, scalene) or by angle (right).

But the heading says: (equilateral / isosceles / scalene / right) — so all four are options.

So possibly, each triangle fits one of these categories, but some may fit more than one.

But since only one blank is provided, we must choose the most appropriate.

Let’s analyze each again with that in mind.

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Final Classification:

1. All sides equal → Equilateral
2. Right angle → Right
3. Two sides equal → Isosceles
4. All sides equal → Equilateral
5. Right angle → Right
6. Right angle AND two equal sides → Can be both Right and Isosceles

But since only one answer is expected, and "right" is a key feature, and "isosceles" is about sides, perhaps the worksheet wants the angle-based classification when applicable.

But in many cases, right triangle takes precedence over isosceles in labeling.

Alternatively, maybe the intention is to classify by side type, and ignore angle unless it's specified.

But the title includes right, so it's included.

Let’s assume the goal is to identify the type using the most defining characteristic.

But to be safe, let’s see what’s typical:

In K-5 geometry, students learn:
- Equilateral: all sides equal
- Isosceles: two sides equal
- Scalene: no sides equal
- Right: has a 90° angle

And a triangle can be right and isosceles, etc.

But in this worksheet, since only one blank is provided, likely they expect one classification.

Now, observe:

- Triangle 6: has a right angle and two equal legs → right isosceles triangle
- But since the options are separate, and "right" is listed, probably "right" is acceptable.

But wait — could it be classified as isosceles? Yes.

But right is more specific to the angle.

But the problem is: which one to choose?

Looking at similar worksheets, usually:
- If it has a right angle, label it right
- Otherwise, label by sides

So even if it's also isosceles, right is the priority.

But triangle 2 and 5 are right triangles with no equal sides, so they are scalene right triangles.

Triangle 6 is isosceles right triangle.

But again, only one label.

So likely, "right" is the intended answer for triangles with a right angle.

But let’s check:

- Triangle 2: right → Right
- Triangle 5: right → Right
- Triangle 6: right → Right

But triangle 3 is isosceles, not right.

So perhaps:

1. Equilateral
2. Right
3. Isosceles
4. Equilateral
5. Right
6. Right

But triangle 6 is also isosceles, but we can’t write two answers.

Alternatively, maybe the worksheet expects side-based classification, and right is just an additional category.

But the instruction says: "Classify the triangles (equilateral / isosceles / scalene / right)"

So it’s open to any of the four.

But since only one line is provided, likely one classification per triangle.

So let’s decide:

- For triangles with a right angle, use "right"
- For others, use side-based classification

So:

1. All sides equal → Equilateral
2. Right angle → Right
3. Two sides equal → Isosceles
4. All sides equal → Equilateral
5. Right angle → Right
6. Right angle → Right

Even though triangle 6 is also isosceles, the presence of a right angle makes it a right triangle, and that’s the main classification.

Alternatively, if the worksheet emphasizes side classification, then triangle 6 would be isosceles.

But it has a right angle, so right is more distinctive.

Let’s compare with standard practice.

In most grade 5 curricula, when a triangle has a right angle, it is classified as right triangle, regardless of side lengths.

So final answers:

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✔ Answers:

1. Equilateral
2. Right
3. Isosceles
4. Equilateral
5. Right
6. Right

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Explanation Summary:

- Equilateral: All three sides are equal (triangles 1 and 4)
- Isosceles: Two sides are equal (triangle 3)
- Right: Has a 90° angle (triangles 2, 5, and 6)
- Scalene: No equal sides — none of the triangles appear to be scalene, so not used here.

Note: Triangle 6 is both isosceles and right, but since the worksheet allows only one answer per triangle, and "right" is a distinct category, we use Right.

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✔ Final Answer:

1. Equilateral
2. Right
3. Isosceles
4. Equilateral
5. Right
6. Right