Have you ever thought of making a tipi? Take a look at this dilemma.
Jaime has been working hard on her tipi. She has decided to use the following pattern as part of the design on the material. She thinks that if she uses cloth triangles, that she can sew them onto the cloth of the tipi to make a pattern. This red, black, red pattern is going to stretch along the outside bottom edge of the tipi.
“That is very cool,” her sister Lily said admiring Jaime’s sketch.
“I think so too. It should look very pretty on the brown material,” Jaime added.
“Yes. How do you know that the triangles will be the exact same size?”
“What kind of triangle is that?” Lily asked.
Do you know? This Concept is all about different types of triangles. As you learn all about the different types of triangles, think about this problem. What type of triangle is in the pattern? Can you justify your answer?
In this Concept, we will examine different kinds of triangles. As you know, triangles are geometric figures that have three sides and three angles. There are different types of triangles too. We can classify or identify them in different ways. One way is by their angles measures and one way is by their sides lengths.
Let’s start with angle measures first.
We all know that triangles have three angles. The corners where each of the line segments connects form an angle. When we know the measures of these angles, we can use this information to name and identify the triangles.
Let’s look at some of the different types of triangles according to angle measure.
Now let's apply this information.
Identify whether each of the following triangles is acute, obtuse or right.
Now let’s break each one down.
The second triangle has three angles that are less than 90 degrees, this is an acute triangle.
The third triangle also has three angles that are less than 90 degrees. This is also an acute triangle.
The fourth triangle has a right angle. You can see that because it forms a nice neat corner so perfectly. This is a right triangle.
The fifth triangle has an angle greater than 90 degrees. This is an obtuse triangle.
We can also classify or identify triangles by the length of their sides. This means that we look at the line segments that create the triangle.
Equilateral Triangles are triangles with all three sides equal.
Isosceles Triangle has two sides that are equal in length. Often an isosceles triangle is the trickiest one to identify.
Scalene Triangles are triangles where none of the sides are the same length. All three sides are different lengths.
Now let’s apply what we have learned and identify some triangles.
Classify each triangle as equilateral, isosceles, or scalene.
We need to examine the lengths of the sides in each triangle to see if any sides are congruent.
In the first triangle, two sides are 7 meters long, but the third side is shorter. Which kind of triangle has two congruent sides? This is an isosceles triangle.
Now let’s look at the second triangle. All three sides are the same length, so this must be an equilateral triangle.
The last triangle has sides of 5.5 cm, 4.1 cm, and 8 cm. None of the sides are congruent, so this is a scalene triangle.
Once you know all of this information, you will find that you can classify a triangle by both its sides and its angles.
Define a scalene triangle.
Solution: A triangle where all of the side lengths are different.
Define an obtuse triangle.
Define an isosceles triangle
Solution: A triangle with two sides of the same length.
Now let's go back to the dilemma from the beginning of the Concept.
What type of triangle is in the pattern? Can you justify your answer?
A triangle where all three angles are less than 90∘.
A triangle with one 90∘ angle and two acute angles.
a triangle with one angle that is greater than 90∘.
all three side lengths and all three angles are congruent.
two side lengths are the same.
all three side lengths are different
means exactly the same, having the same measure.
Here is one for you to try on your own.
Identify each triangle by both its sides and angles.
The first triangle is a right isosceles triangle. It has one right angle and two sides that are the same length.
The second triangle is an acute scalene triangle. All three sides are different lengths and all three angle measures are acute.
The third triangle is an obtuse scalene triangle. It has one obtuse angle and three different side lengths.
The last triangle is an obtuse isosceles. It has one obtuse angle and two side lengths that are the same.
Directions: Classify each triangle by the given angle measures as acute, obtuse or right.
- A triangle with three 60∘ angles.
- A triangle with one 110∘ angle.
- A triangle with one right angle and two acute angles.
- A triangle with one 130∘ angle.
- A triangle with three acute angles.
- A triangle with a 90∘ angle.
- A triangle with three angles that are less than 90∘
Directions: Identify each triangle by the side lengths described. Identify them as equilateral, isosceles or scalene.
- A triangle with side lengths of 6 in, 6 in and 4 inches.
- A triangle with side lengths of 3 ft, 4 ft, and 5 ft.
- A triangle with side lengths of 8 inches.
- A triangle with side lengths of 7 inches, 8 inches and 8 inches.
- A triangle with side lengths of 6 meters, 8 meters and 10 meters.
- A triangle with side lengths of 10 mm.
- A triangle with side lengths of 12 cm.