Identify triangles based on their angles and sides in this educational worksheet.
Worksheet titled "Identifying Triangles" with various triangle diagrams and labels for classification based on angles and sides.
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Step-by-step solution for: Classifying Triangles based on Sides and Angles Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Classifying Triangles based on Sides and Angles Worksheets
To identify each triangle, we need to look at two things: the angles and the sides.
1. Classifying by Angles:
* Acute Triangle: All three angles are less than 90°.
* Right Triangle: One angle is exactly 90° (often marked with a small square).
* Obtuse Triangle: One angle is greater than 90°.
2. Classifying by Sides:
* Equilateral Triangle: All three sides have the same length.
* Isosceles Triangle: At least two sides have the same length (marked with tick marks or equal numbers).
* Scalene Triangle: No sides have the same length.
Now, let's analyze each triangle one by one based on the markings and labels in the worksheet:
* Triangle 1: The text below it already says "Acute Isosceles Triangle." Let's verify. It has tick marks on two sides, meaning they are equal (Isosceles). All angles look sharp and less than 90° (Acute).
* Answer: Acute Isosceles Triangle
* Triangle 2: There is a small square symbol in the corner. This means it has a 90° angle (Right). The sides have different lengths (no matching tick marks or numbers), so it is Scalene.
* Answer: Right Scalene Triangle
* Triangle 3: There is a small square symbol indicating a 90° angle (Right). Two sides have tick marks showing they are equal length (Isosceles).
* Answer: Right Isosceles Triangle
* Triangle 4: One angle is clearly wider than a corner of a square (obtuse). The sides all appear to be different lengths (Scalene).
* Answer: Obtuse Scalene Triangle
* Triangle 5: All three sides have a single tick mark, meaning they are all equal (Equilateral). Because all sides are equal, all angles must be 60°, which is acute.
* Answer: Acute Equilateral Triangle
* Triangle 6: One angle is very wide, definitely more than 90° (Obtuse). Two sides have tick marks indicating they are equal (Isosceles).
* Answer: Obtuse Isosceles Triangle
* Triangle 7: All angles look sharp and less than 90° (Acute). The sides have different lengths (Scalene).
* Answer: Acute Scalene Triangle
* Triangle 8: There is a small square symbol for a 90° angle (Right). The sides have different lengths (Scalene).
* Answer: Right Scalene Triangle
* Triangle 9: One angle is wide and obtuse (>90°). The sides are all different lengths (Scalene).
* Answer: Obtuse Scalene Triangle
* Triangle 10: There is a small square symbol for a 90° angle (Right). Two sides have tick marks showing they are equal (Isosceles).
* Answer: Right Isosceles Triangle
* Triangle 11: All angles are sharp and less than 90° (Acute). Two sides have tick marks showing they are equal (Isosceles).
* Answer: Acute Isosceles Triangle
* Triangle 12: All angles are sharp and less than 90° (Acute). All three sides have tick marks showing they are equal (Equilateral).
* Answer: Acute Equilateral Triangle
Final Answer:
1. Acute Isosceles Triangle
2. Right Scalene Triangle
3. Right Isosceles Triangle
4. Obtuse Scalene Triangle
5. Acute Equilateral Triangle
6. Obtuse Isosceles Triangle
7. Acute Scalene Triangle
8. Right Scalene Triangle
9. Obtuse Scalene Triangle
10. Right Isosceles Triangle
11. Acute Isosceles Triangle
12. Acute Equilateral Triangle
1. Classifying by Angles:
* Acute Triangle: All three angles are less than 90°.
* Right Triangle: One angle is exactly 90° (often marked with a small square).
* Obtuse Triangle: One angle is greater than 90°.
2. Classifying by Sides:
* Equilateral Triangle: All three sides have the same length.
* Isosceles Triangle: At least two sides have the same length (marked with tick marks or equal numbers).
* Scalene Triangle: No sides have the same length.
Now, let's analyze each triangle one by one based on the markings and labels in the worksheet:
* Triangle 1: The text below it already says "Acute Isosceles Triangle." Let's verify. It has tick marks on two sides, meaning they are equal (Isosceles). All angles look sharp and less than 90° (Acute).
* Answer: Acute Isosceles Triangle
* Triangle 2: There is a small square symbol in the corner. This means it has a 90° angle (Right). The sides have different lengths (no matching tick marks or numbers), so it is Scalene.
* Answer: Right Scalene Triangle
* Triangle 3: There is a small square symbol indicating a 90° angle (Right). Two sides have tick marks showing they are equal length (Isosceles).
* Answer: Right Isosceles Triangle
* Triangle 4: One angle is clearly wider than a corner of a square (obtuse). The sides all appear to be different lengths (Scalene).
* Answer: Obtuse Scalene Triangle
* Triangle 5: All three sides have a single tick mark, meaning they are all equal (Equilateral). Because all sides are equal, all angles must be 60°, which is acute.
* Answer: Acute Equilateral Triangle
* Triangle 6: One angle is very wide, definitely more than 90° (Obtuse). Two sides have tick marks indicating they are equal (Isosceles).
* Answer: Obtuse Isosceles Triangle
* Triangle 7: All angles look sharp and less than 90° (Acute). The sides have different lengths (Scalene).
* Answer: Acute Scalene Triangle
* Triangle 8: There is a small square symbol for a 90° angle (Right). The sides have different lengths (Scalene).
* Answer: Right Scalene Triangle
* Triangle 9: One angle is wide and obtuse (>90°). The sides are all different lengths (Scalene).
* Answer: Obtuse Scalene Triangle
* Triangle 10: There is a small square symbol for a 90° angle (Right). Two sides have tick marks showing they are equal (Isosceles).
* Answer: Right Isosceles Triangle
* Triangle 11: All angles are sharp and less than 90° (Acute). Two sides have tick marks showing they are equal (Isosceles).
* Answer: Acute Isosceles Triangle
* Triangle 12: All angles are sharp and less than 90° (Acute). All three sides have tick marks showing they are equal (Equilateral).
* Answer: Acute Equilateral Triangle
Final Answer:
1. Acute Isosceles Triangle
2. Right Scalene Triangle
3. Right Isosceles Triangle
4. Obtuse Scalene Triangle
5. Acute Equilateral Triangle
6. Obtuse Isosceles Triangle
7. Acute Scalene Triangle
8. Right Scalene Triangle
9. Obtuse Scalene Triangle
10. Right Isosceles Triangle
11. Acute Isosceles Triangle
12. Acute Equilateral Triangle
Parent Tip: Review the logic above to help your child master the concept of classifying triangles by angles worksheet.