Problem Analysis:
The task involves identifying different types of triangles based on their angles and side lengths. Here are the key definitions we need to use:
1.
Acute Triangle: All angles are less than 90°.
2.
Right Triangle: One angle is exactly 90°.
3.
Obtuse Triangle: One angle is greater than 90°.
4.
Equilateral Triangle: All three sides are equal, and all angles are 60°.
5.
Isosceles Triangle: Two sides are equal.
6.
Scalene Triangle: No sides are equal.
We will analyze each triangle in the image and match it with the given descriptions.
---
Step-by-Step Solution:
#### Triangles in the Image:
1.
Triangle A:
- One angle is 90° (right angle).
- All sides are of different lengths.
-
Type: Right-angled scalene triangle.
2.
Triangle B:
- One angle is 90° (right angle).
- Two sides are marked as equal.
-
Type: Right-angled isosceles triangle.
3.
Triangle C:
- All angles are less than 90° (acute angles).
- All sides are marked as equal.
-
Type: Equilateral triangle.
4.
Triangle D:
- One angle is greater than 90° (obtuse angle).
- Two sides are marked as equal.
-
Type: Obtuse-angled isosceles triangle.
5.
Triangle E:
- One angle is greater than 90° (obtuse angle).
- All sides are of different lengths.
-
Type: Obtuse-angled scalene triangle.
6.
Triangle F:
- All angles are less than 90° (acute angles).
- Two sides are marked as equal.
-
Type: Acute-angled isosceles triangle.
---
#### Answering the Questions:
1.
Name the triangle which is acute angled as well as isosceles.
- From the analysis,
Triangle F is acute-angled and isosceles.
-
Answer: F
2.
Name the triangle which is right angled triangle as well as scalene.
- From the analysis,
Triangle A is right-angled and scalene.
-
Answer: A
3.
Name the triangle which is scalene as well as acute angled.
- From the analysis, there is no triangle that is both scalene and acute-angled in the given set. However, if we assume a hypothetical scenario or misinterpretation, we can note that none fits this description perfectly based on the provided images.
-
Answer: None (or re-evaluate if additional context is needed).
4.
Name the triangle which is obtuse angled as well as isosceles.
- From the analysis,
Triangle D is obtuse-angled and isosceles.
-
Answer: D
5.
Name the triangle which is obtuse angled as well as scalene.
- From the analysis,
Triangle E is obtuse-angled and scalene.
-
Answer: E
6.
Name the triangle which is equilateral.
- From the analysis,
Triangle C is equilateral.
-
Answer: C
---
Final Answers:
\[
\boxed{
\begin{array}{ll}
\text{a) } & \text{A} \\
\text{b) } & \text{None} \\
\text{c) } & \text{D} \\
\text{d) } & \text{E} \\
\text{e) } & \text{C} \\
\end{array}
}
\]
If there is any ambiguity or need for further clarification, please let me know!
Parent Tip: Review the logic above to help your child master the concept of triangles worksheet 5th grade.
