Triangles Exploration
Today, you will complete an exploration about triangles. You will investigate the following essential questions:
Vocabulary terms
Congruent = Figures that are the same size and the same shape; Angles that have the same measure.
Polygon = A closed figure with straight sides that intersect at points called vertices.
Vertex = The point of intersection of two lines, rays, or line segments.
- What are common properties of all triangles?
- How are triangles classified (named)?
Vocabulary terms
Congruent = Figures that are the same size and the same shape; Angles that have the same measure.
Polygon = A closed figure with straight sides that intersect at points called vertices.
Vertex = The point of intersection of two lines, rays, or line segments.
What are common properties of all triangles?
Triangles are defined as polygons with three sides and three interior (inside) angles. That means all triangles are closed figures (no openings or holes) that have straight sides (no curves) that intersect at corners called vertices (the plural of vertex).
Let's look more closely at the two main properties of triangles: their side lengths and their interior angles.
Task 1: Explore using the applet below (click to activate it). Try changing the angles and side lengths by dragging the vertices. Look closely at the angles on the straight line below the triangle. What do you notice? Look at the side lengths in the table. Do you notice anything?
Triangles are defined as polygons with three sides and three interior (inside) angles. That means all triangles are closed figures (no openings or holes) that have straight sides (no curves) that intersect at corners called vertices (the plural of vertex).
Let's look more closely at the two main properties of triangles: their side lengths and their interior angles.
Task 1: Explore using the applet below (click to activate it). Try changing the angles and side lengths by dragging the vertices. Look closely at the angles on the straight line below the triangle. What do you notice? Look at the side lengths in the table. Do you notice anything?
Task 2: Try this next animation from Geogebra. Change the size of the triangle and slowly move the slider. What do you notice about the sum (total) of the angles? Try several sizes and shapes of triangles. Is this always true? You may want to try this animation, too, to get a better look at the sum of the angles.
How are triangles classified (named)?
Clearly, there are many different ways to draw a triangle. How can we give every triangle a name?
Task 3: Explore using this triangle sorting activity. Try to sort all the triangles into several groups. How did you sort them? Can you sort them a different way?
Task 4: Watch this video from Mr. Bowen about how triangles are classified.
To review, a triangle is given two names: one based on its side lengths and one based on its interior angles. Think of this like a triangle's first and last name. Its first name is given according to its sides:
Note: equilateral literally means "equal sides", isoseles means "equal legs" and scalene means "uneven" or "odd".
A triangle's last name is given according to its angles:
A triangle's last name is given according to its angles:
Examine this diagram of the types of triangles. Do you notice anything?
Task 5: Experiment creating triangles with this interactive from Geogebra. Can you make every type of triangle?
Task 6: Are you ready to test your ability to classify triangles? Take the Types of Triangles Challenge. There are multiple levels. Think carefully!
Task 7: Reflect on what you have learned about triangles by completing this response form in Google Forms. Be sure to answer every question. Click submit when you are finished.
Task 8: Try these review games. You may have to click "enable flash" to begin.
Task 7: Reflect on what you have learned about triangles by completing this response form in Google Forms. Be sure to answer every question. Click submit when you are finished.
Task 8: Try these review games. You may have to click "enable flash" to begin.
