Identify the Type for Each Triangle - Worksheet with 12 triangles to classify by side lengths and angles.
Worksheet for identifying triangle types with 12 labeled triangles, each with sides marked a, b, c, or s, and spaces to write the type of triangle (e.g., right, isosceles, equilateral).
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Show Answer Key & Explanations
Step-by-step solution for: Geometry Worksheets | Triangle Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Geometry Worksheets | Triangle Worksheets
To identify the type of each triangle, we look at two things:
1. Angles: Does it have a right angle (90 degrees)? If yes, it's a Right triangle.
2. Sides: Are the sides equal?
* All 3 sides equal = Equilateral.
* Exactly 2 sides equal = Isosceles.
* No sides equal = Scalene.
Here is the step-by-step identification for each number:
1) Right Scalene: It has a square symbol indicating a right angle. The sides are labeled a, b, and c, which usually means they are all different lengths.
2) Scalene: There is no right angle mark. The sides are labeled a, b, and c, meaning all three sides are different lengths.
3) Scalene: Similar to #2, sides a, b, and c indicate all sides are different lengths.
4) Isosceles: Sides 'a' and 'b' are labeled. In geometry problems like this, if two sides share a variable label distinct from the third, or if they look symmetric, it implies they are equal. Wait, looking closer at standard conventions for these worksheets: usually, if sides are labeled with different letters (a, b, c), they are scalene. If two sides have the same letter (like 'b' and 'b'), they are isosceles. If all three have the same letter (like 's', 's', 's'), they are equilateral.
* Let's re-evaluate based on the labels provided in the image strictly.
* #1: Right angle. Sides a, b, c. Since a, b, c are distinct variables, we assume sides are unequal unless marked otherwise. So, Right Scalene.
* #2: Sides a, b, c. All different. Scalene.
* #3: Sides a, b, c. All different. Scalene.
* #4: Sides a, b, c. All different. Scalene. (Note: Visually it looks isosceles, but the labels a, b, c suggest scalene. However, often in these diagrams, if it looks isosceles but isn't labeled as such, it might be tricky. Let's look at #6. #6 has 'b' and 'b'. That is definitely Isosceles. #9 has 's', 's', 's'. That is Equilateral. Therefore, the labels are the key. If labels are different, sides are different.)
* #5: Sides a, b, c. All different. Scalene.
* #6: Sides are labeled 'b', 'b', and 'a'. Two sides are equal ('b'). Isosceles.
* #7: Has a right angle. Sides are 'a', 'a', and 'c'. Two sides are equal ('a'). Right Isosceles.
* #8: Sides are 'b', 'b', and 'a'. Two sides are equal ('b'). Isosceles.
* #9: Sides are 's', 's', and 's'. All three sides are equal. Equilateral.
* #10: Sides are 's', 's', and 's'. All three sides are equal. Equilateral.
* #11: Sides are 'b', 'b', and 'a'. Two sides are equal ('b'). Isosceles.
* #12: Has a right angle. Sides are 'a', 'b', and 'c'. All labels are different. Right Scalene.
Let's double check #4 and #5. They look like obtuse triangles. But without angle measures, we classify by sides primarily if angles aren't given, or just "Obtuse" if that's an option. The prompt asks for "Type". Usually, this means side classification (Scalene, Isosceles, Equilateral) or angle classification (Right, Acute, Obtuse). Given #1 and #7 explicitly show right angles, and #9/#10 show equilateral sides, the worksheet mixes these.
* Triangles with specific side marks (like s,s,s or b,b,a) are classified by sides.
* Triangles with right angle marks are classified as Right.
* What about #2, #3, #4, #5? They have no right angle mark and all different side labels (a,b,c). They are Scalene. (They could also be described as Acute or Obtuse, but Scalene is the definitive side type derived from the labels).
Let's refine the answers to be the most standard "Type" expected in this grade level context.
1. Right Scalene (Has right angle, sides a,b,c)
2. Scalene (Sides a,b,c)
3. Scalene (Sides a,b,c)
4. Scalene (Sides a,b,c) - *Visually obtuse, but labels dictate scalene*
5. Scalene (Sides a,b,c) - *Visually obtuse, but labels dictate scalene*
6. Isosceles (Sides b,b,a)
7. Right Isosceles (Has right angle, sides a,a,c)
8. Isosceles (Sides b,b,a)
9. Equilateral (Sides s,s,s)
10. Equilateral (Sides s,s,s)
11. Isosceles (Sides b,b,a)
12. Right Scalene (Has right angle, sides a,b,c)
Final Answer:
1) Right Scalene
2) Scalene
3) Scalene
4) Scalene
5) Scalene
6) Isosceles
7) Right Isosceles
8) Isosceles
9) Equilateral
10) Equilateral
11) Isosceles
12) Right Scalene
1. Angles: Does it have a right angle (90 degrees)? If yes, it's a Right triangle.
2. Sides: Are the sides equal?
* All 3 sides equal = Equilateral.
* Exactly 2 sides equal = Isosceles.
* No sides equal = Scalene.
Here is the step-by-step identification for each number:
1) Right Scalene: It has a square symbol indicating a right angle. The sides are labeled a, b, and c, which usually means they are all different lengths.
2) Scalene: There is no right angle mark. The sides are labeled a, b, and c, meaning all three sides are different lengths.
3) Scalene: Similar to #2, sides a, b, and c indicate all sides are different lengths.
4) Isosceles: Sides 'a' and 'b' are labeled. In geometry problems like this, if two sides share a variable label distinct from the third, or if they look symmetric, it implies they are equal. Wait, looking closer at standard conventions for these worksheets: usually, if sides are labeled with different letters (a, b, c), they are scalene. If two sides have the same letter (like 'b' and 'b'), they are isosceles. If all three have the same letter (like 's', 's', 's'), they are equilateral.
* Let's re-evaluate based on the labels provided in the image strictly.
* #1: Right angle. Sides a, b, c. Since a, b, c are distinct variables, we assume sides are unequal unless marked otherwise. So, Right Scalene.
* #2: Sides a, b, c. All different. Scalene.
* #3: Sides a, b, c. All different. Scalene.
* #4: Sides a, b, c. All different. Scalene. (Note: Visually it looks isosceles, but the labels a, b, c suggest scalene. However, often in these diagrams, if it looks isosceles but isn't labeled as such, it might be tricky. Let's look at #6. #6 has 'b' and 'b'. That is definitely Isosceles. #9 has 's', 's', 's'. That is Equilateral. Therefore, the labels are the key. If labels are different, sides are different.)
* #5: Sides a, b, c. All different. Scalene.
* #6: Sides are labeled 'b', 'b', and 'a'. Two sides are equal ('b'). Isosceles.
* #7: Has a right angle. Sides are 'a', 'a', and 'c'. Two sides are equal ('a'). Right Isosceles.
* #8: Sides are 'b', 'b', and 'a'. Two sides are equal ('b'). Isosceles.
* #9: Sides are 's', 's', and 's'. All three sides are equal. Equilateral.
* #10: Sides are 's', 's', and 's'. All three sides are equal. Equilateral.
* #11: Sides are 'b', 'b', and 'a'. Two sides are equal ('b'). Isosceles.
* #12: Has a right angle. Sides are 'a', 'b', and 'c'. All labels are different. Right Scalene.
Let's double check #4 and #5. They look like obtuse triangles. But without angle measures, we classify by sides primarily if angles aren't given, or just "Obtuse" if that's an option. The prompt asks for "Type". Usually, this means side classification (Scalene, Isosceles, Equilateral) or angle classification (Right, Acute, Obtuse). Given #1 and #7 explicitly show right angles, and #9/#10 show equilateral sides, the worksheet mixes these.
* Triangles with specific side marks (like s,s,s or b,b,a) are classified by sides.
* Triangles with right angle marks are classified as Right.
* What about #2, #3, #4, #5? They have no right angle mark and all different side labels (a,b,c). They are Scalene. (They could also be described as Acute or Obtuse, but Scalene is the definitive side type derived from the labels).
Let's refine the answers to be the most standard "Type" expected in this grade level context.
1. Right Scalene (Has right angle, sides a,b,c)
2. Scalene (Sides a,b,c)
3. Scalene (Sides a,b,c)
4. Scalene (Sides a,b,c) - *Visually obtuse, but labels dictate scalene*
5. Scalene (Sides a,b,c) - *Visually obtuse, but labels dictate scalene*
6. Isosceles (Sides b,b,a)
7. Right Isosceles (Has right angle, sides a,a,c)
8. Isosceles (Sides b,b,a)
9. Equilateral (Sides s,s,s)
10. Equilateral (Sides s,s,s)
11. Isosceles (Sides b,b,a)
12. Right Scalene (Has right angle, sides a,b,c)
Final Answer:
1) Right Scalene
2) Scalene
3) Scalene
4) Scalene
5) Scalene
6) Isosceles
7) Right Isosceles
8) Isosceles
9) Equilateral
10) Equilateral
11) Isosceles
12) Right Scalene
Parent Tip: Review the logic above to help your child master the concept of triangles math worksheet.
