Let's complete the table based on the provided information.
### Table Completion
We are given information about three specific triangles: an equilateral triangle, an isosceles triangle, and a scalene triangle. Below is the completed table with the names of the triangles, their angles, and the sides:
[tex]\[
\begin{array}{|c|l|l|l|l|}
\hline
\text{No} & \text{20 shape} & \text{Name of the Triangle} & \text{Angles of the Triangle} & \text{Sides of the Triangle} \\
\hline
1.1.1 & & \text{Equilateral} & [60^\circ, 60^\circ, 60^\circ] & [a, b, c] \\
\hline
1.1.2 & & \text{Isosceles} & [70^\circ, 70^\circ, 40^\circ] & [a, b, b] \\
\hline
1.1.3 & & \text{Scalene} & [50^\circ, 60^\circ, 70^\circ] & [a, b, c] \\
\hline
\end{array}
\][/tex]
### Explanation
1. Equilateral Triangle:
- Name of the Triangle: Equilateral
- Angles of the Triangle: An equilateral triangle has three equal angles, each measuring 60 degrees.
- Sides of the Triangle: All three sides are of equal length, usually denoted as [tex]\(a, b, c\)[/tex], where [tex]\(a = b = c\)[/tex].
2. Isosceles Triangle:
- Name of the Triangle: Isosceles
- Angles of the Triangle: An isosceles triangle has two equal angles and one different angle. In this example, the angles are 70 degrees, 70 degrees, and 40 degrees.
- Sides of the Triangle: It has two equal sides. Let’s denote the sides as [tex]\(a, b, b\)[/tex], where [tex]\(b\)[/tex] is the length of the two equal sides.
3. Scalene Triangle:
- Name of the Triangle: Scalene
- Angles of the Triangle: A scalene triangle has all three angles different. The angles in this example are 50 degrees, 60 degrees, and 70 degrees.
- Sides of the Triangle: All three sides are of different lengths, denoted as [tex]\(a, b, c\)[/tex], where [tex]\(a \neq b \neq c\)[/tex].
This completes the investigation of angles and sides for the given triangles.
