Lesson Overview
In this lesson, students will learn what triangles are, explore their properties, and discover the different types of triangles based on their sides and angles. Students will also use Ziggy to construct triangles and observe that the sum of interior angles in any triangle is always 180°.
What You Will Learn
•
Understand the concept of a triangle
•
Explore the properties of triangles
•
Learn how to calculate missing angles
•
Identify different types of triangles
•
Use Ziggy to construct triangles
Exploring Triangles in Geometry
A triangle is a geometric shape made of three connected line segments. It is a two-dimensional closed shape that can have different side lengths and angles.
Triangles Around Us
Triangles appear in many real-life objects because they are strong and stable. Examples include :
1.
Roofs (gables)
2.
Bridges
3.
Pizza slices
4.
Nachos
5.
Birthday caps
Properties of a Triangle
A triangle has the following properties:
•
Three sides, three angles, and three vertices
•
The sum of all interior angles = 180°
•
The sum of any two sides is greater than the third side
•
The largest angle is opposite the longest side
•
An exterior angle equals the sum of the two opposite interior angles
Angles of a Triangle
If two angles of a triangle are known, the third angle can be calculated using the formula:
180° − (sum of known angles)
Examples:
•
100° + 40° + 40° = 180°
•
120° + 10° + 50° = 180°
Types of Triangles
Classification of Triangles
Triangles can be classified:
•
By side length
•
By angle measure
Types of Triangles by Angles
Acute Triangle:
All angles < 90°
All angles < 90°
Right Triangle: One angle = 90°
Obtuse Triangle: One angle > 90°
Types of Triangles by Sides
Scalene Triangle
•
All sides have different lengths
•
All angles are different
Isosceles Triangle
•
Two sides are equal
•
Two angles are equal
•
Equal sides are called legs
•
The unequal side is called the base
Equilateral Triangle
•
All sides are equal
•
All angles = 60°
Constructing Triangles with Ziggy
Triangles can be constructed using geometry rules. With Ziggy, we use movement, turning, and angles to draw different triangles.
You can use the following website to calculate the triangle sides and angles by providing 3 inputs.
Activity 1: Constructing a Scalene Triangle
Sides: 106.6 mm , 71 mm, 100 mm ( Rounded )
Interior Angles: 40°, 65°, 75°
Note: We use exterior angles when drawing using Ziggy
Exterior Angles: 140°, 115°, 105°
Create the following Code, download and test
Activity 2: Constructing an Isosceles Triangle
Equal Sides: 60 mm
Base: 40 mm
Angles: 70.5°, 70.5°, 39° ( Rounded )
Note: We use exterior angles when drawing using Ziggy
Exterior Angles: 109.5°, 109.5°, 141°
Make the following code to draw the isosceles triangle:
Activity 3: Constructing an Equilateral Triangle
All sides: 100 mm
All angles: 60° ( exterior 120° )
Make the following code to draw the equilateral triangle
Challenge
Use Ziggy to draw a house. Try different solutions and use repeat blocks.
