4.04 Triangles and Angles

Triangles and Angles

Remember that in the previous lesson we learned that the polygon with the smallest number of sides is called a triangle. We will begin our in-depth study of the triangle.

triangle
interior angle
exterior angle
scalene triangle
isosceles triangle
equilateral triangle
acute triangle
obtuse triangle
right triangle
equiangular triangle

Classify Triangles by Sides

We know that a triangle has three sides.

Remember congruent ≅ means equal in measure!

Scalene Triangle - no sides congruent

A triangle where clearly none of the sides have the same length

Equilateral Triangle - all three sides congruent

A triangle where each side has a small dash through the middle, marking the 3 sides as congruent

Isosceles Triangle - at least two sides congruent

A triangle where 2 sides have a small dash through the middle, marking the 2 sides as congruent. The third side in much longer

Complete this Geogebra activity to find out more about types of triangles, their sides, and angles.

Your Turn

Classify the triangle as:

Scalene Triangle
Isosceles Triangle
Equilateral Triangle

A triangle forming the roof of a colosseum. The top two sides appear similar length, and the base side is very long

Answer: Isosceles

Classify the triangle as:

Scalene Triangle
Isosceles Triangle
Equilateral Triangle

a traffic yield sign. All sides appear similar length

Answer: Equilateral

Classify the triangle as:

Scalene Triangle
Isosceles Triangle
Equilateral Triangle

A decorative dagger where none of the sides seem to have similar lengths

Answer: Scalene

Recall Angles

m∠A is read as measure of angle A

Acute Angle - measures less than 90°

47 degree angle

Right Angle - measures 90°

90 degree angle

Obtuse Angle - measures more than 90° but less than 180°

144 degree angle

We know that a triangle has three angles.

Remember congruent ≅ means equal in measure!

Acute Triangle - three acute angles

A triangle with a 62 degree angle, a 64 degree angle, and a 54 degree angle

Equiangular Triangle - three acute angles 60° each

A triangle with 3 angles measuring 60 degrees each

Obtuse Triangle - one obtuse angle

A triangle with an 115 degree angle. The other angles are not marked with values

Right Triangle - one right angle

A triangle with a 90 degree angle. The other angles are not marked with values

Acute Versus Equiangular

Note that an equiangular triangle is also known as acute. Just in this case, all three angles are ≅. since equiangular is more descriptive, we say it is equiangular.

Acute Triangle - three acute angles

A triangle with 3 angles measuring 60 degrees each

Equiangular Triangle - three acute angles 60° each

Your Turn

Classify the triangle as:

Acute Triangle
Obtuse Triangle
Equiangular Triangle
Right Triangle

A triangle where all three angles appear smaller than a right angle

Answer: Acute

Classify the triangle as:

Acute Triangle
Obtuse Triangle
Equiangular Triangle
Right Triangle

A triangle where all three angles are marked as equal value

Answer: Equiangular

Classify the triangle as:

Acute Triangle
Obtuse Triangle
Equiangular Triangle
Right Triangle

A triangle where 1 of the angles appears to be greater than 90 degrees

Answer: Obtuse

Classify the triangle as:

Acute Triangle
Obtuse Triangle
Equiangular Triangle
Right Triangle

A triangle with a one angle with value 90 degrees

Answer: Right

Equilateral - Equiangular

If you know the triangle is equilateral then you can assume it is equiangular. Also, if you know the triangle is equiangular then you know if it equilateral.

Equilateral Triangle - all three sides congruent

A triangle where all three sides are 5 inches and all three angles are 60 degrees

Equiangular Triangle - three acute angles 60° each

Your Turn

Now classify the triangle by its sides and angles.

Sides:

Scalene
Isosceles
Equilateral

Angles:

Acute
Obtuse
Equiangular
Right

A triangle with a 90 degree angle

Answer: Scalene & Right

Now classify the triangle by its sides and angles.

Sides:

Scalene
Isosceles
Equilateral

Angles:

Acute
Obtuse
Equiangular
Right

A triangle with an 126 degree angle. The sides adjacent to that angle are both 3

Answer: Isosceles & Obtuse

Now classify the triangle by its sides and angles.

Sides:

Scalene
Isosceles
Equilateral

Angles:

Acute
Obtuse
Equiangular
Right

A triangle where all 3 angles have different degree measures below 90 and all 3 sides have different lengths

Answer: Scalene & Acute