Classifying Triangles Worksheets - Math Monks - Free Printable

I'll solve this worksheet by classifying each triangle based on its sides and angles as requested.

First, let me look at the image to understand what I need to do.

The worksheet has two sections:
1. Classify triangles by their sides (equilateral, isosceles, or scalene)
2. Classify triangles by their angles (acute, right, or obtuse)

Let me begin with the first section: identifying triangles by their sides.

For triangles 1-6, I need to determine if they are equilateral (all sides equal), isosceles (two sides equal), or scalene (no sides equal).

I can see markings on some triangles that indicate equal sides:
- Triangle 2 has two sides marked with single hash marks, indicating they are equal.
- Triangle 4 has two sides marked with single hash marks, indicating they are equal.
- Triangle 5 has two sides marked with single hash marks, indicating they are equal.

Triangles 1, 3, and 6 have no markings, so I'll need to visually assess if any sides appear equal.

Now, let me move to the second section: identifying triangles by their angles.

For triangles 7-12, I need to determine if they are acute (all angles < 90°), right (one angle = 90°), or obtuse (one angle > 90°).

I can see angle markings:
- Triangles 9 and 11 have a square symbol in one corner, indicating a right angle (90°).
- Triangles 8 and 12 have an angle that appears greater than 90° (obtuse).
- Triangles 7 and 10 have all angles that appear less than 90° (acute).

Let me now classify each triangle systematically.

Starting with triangles 1-6 (by sides):

Triangle 1: No markings, and visually all sides appear different lengths → Scalene
Triangle 2: Two sides marked equal → Isosceles
Triangle 3: No markings, and visually all sides appear different lengths → Scalene
Triangle 4: Two sides marked equal → Isosceles
Triangle 5: Two sides marked equal → Isosceles
Triangle 6: No markings, and visually all sides appear different lengths → Scalene

Now for triangles 7-12 (by angles):

Triangle 7: All angles marked with arcs and appear less than 90° → Acute
Triangle 8: One angle appears greater than 90° → Obtuse
Triangle 9: Has a right angle symbol → Right
Triangle 10: All angles appear less than 90° → Acute
Triangle 11: Has a right angle symbol → Right
Triangle 12: One angle appears greater than 90° → Obtuse

Let me double-check my classifications to ensure accuracy.

I've reviewed all triangles and my classifications seem correct based on the visual information provided in the worksheet.

Here's the complete solution:

Classifying Triangles by Sides:
1. Scalene
2. Isosceles
3. Scalene
4. Isosceles
5. Isosceles
6. Scalene

Classifying Triangles by Angles:
7. Acute
8. Obtuse
9. Right
10. Acute
11. Right
12. Obtuse