Let’s Learn!
Angles in Triangles
Goal:
Goal:
Think About It!
Goal: Use angles to define triangles.
Triangles can be defined by the angles that they contain. Let’s review the three main types of angles. Look at each angle type below. Think of a definition and sketch one in your notes. Then, click the angle to check your work.
A right angle is an angle that forms a square corner and measures 90 degrees.
An acute angle is an angle that is greater than 0 degrees and less than 90 degrees.
An obtuse angle is an angle that is greater than 90 degrees.
Daniel noticed that in some pictures of the Mediterranean Sea, there are a lot of sailboats! Look at this boat with the triangle sail. A triangle is a polygon with 3 sides and 3 angles. Each pair of sides joins at a vertex.
In pictures, Daniel sees all types of triangular sails on the sailboats. Can you guess what kinds of triangles they are based on the angles in them? Click on the sails on the sailboats to see what kinds of triangles Daniel sees.
This boat has two sails that are right triangles.
Right Triangle
A right triangle is a triangle with one right angle and two acute angles. A right angle is a square corner, or 90 degrees. An acute angle is an angle less than 90 degrees.
This sailboat has sails that are acute triangles.
Acute Triangle
An acute triangle is a triangle with three acute angles, or three angles that are less than 90 degrees.
The wind sure is blowing those sails! These sails look like obtuse triangles.
Obtuse Triangle
An obtuse triangle has one obtuse angle, or an angle that is greater than 90 degrees. The other two angles are acute angles.
Question
Look at the sailboat. What kinds of triangles are the sails?
The triangles both have one obtuse angle. They are obtuse triangles.
Daniel sees other triangles that are named by the length of their sides. Click on the sailboats to learn about scalene, isosceles, and equilateral triangles.
This sailboat has two scalene triangles as sails.
Scalene Triangle
A scalene triangle is a triangle in which none of the sides have the same length. Notice that the hash marks are all different. One side has one hash mark, one side has two, and one side has three. That means the sides are all different lengths.
This sailboat has isosceles as sails.
Isosceles Triangle
An isosceles has two sides that are the same length. Notice the hash marks on two of the sides. Those two sides are the same length.
This sailboat has equilateral triangles as sails.
Equilateral Triangle
An equilateral triangle is a triangle in which all three sides are the same length. Notice the hash marks on each side. Those indicate that the sides are the same length.
Question
Look at this sailboat. Study the highlighted sail. What type of triangle is this sail?
The sail is an isosceles triangle. It has two sides that are the same length.
Now that Daniel knows the six types of triangles, he is ready to explore more places where he can see triangles!