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Course: Basic geometry and measurement>Unit 4

Lesson 2: Classifying triangles

Types of triangles review

Review ways to classify triangles based on their sides lengths and angles.  Practice classifying triangles.

Classifying triangles by their angles

Acute triangles

An $\text{acute}$ triangle has $\text{3 angles that}$ . Below are examples of $\text{acute triangles}$.

Right triangles

A $\text{right}$ triangle has and $2$ acute angles. Below are examples of $\text{right triangles}$.

Obtuse triangles

An $\text{obtuse}$ triangle has $\text{one angle that measures}$ and $2$ acute angles. Below are examples of $\text{obtuse triangles}$.
Problem 1A
Classify $\mathrm{△}PQR$ by its angles.

Want to try more problems like this? Check out this exercise

Classifying triangles by their side lengths

Equilateral triangles

An $\text{equilateral}$ triangle has $\text{three equal sides}$. Below are examples of $\text{equilateral}$ triangles.

Isosceles triangles

An $\text{isosceles}$ triangle has $\underset{―}{\text{at least}}$ $\text{two equal sides}$. Below are examples of $\text{isosceles}$ triangles.

Scalene triangles

A $\text{scalene}$ triangle has $\text{no equal sides}$. Below are examples of $\text{scalene}$ triangles.
Problem 2A
Classify $\mathrm{△}PQR$ by its sides.

Want to try more problems like this? Check out this exercise.

Want to join the conversation?

• Why can't I go back to selecting? I got a wrong and I can't go back
• It just won't let you.
• why is the isosceles triangle and the equilateral both classified as each other
• because an equilateral triangle is all equill sides and an isosceles triangle is two or more equill sides
• Is their any more triangle practices?
• No. You will have to do them over if you want extra practice.
• Why are triangles used in math?
• it is because it uses geometry
• I don’t understand why an equilateral triangle is constantly being defined as and Isosceles triangle.
• An equilateral triangle has 3 equal length sides. An isosceles triangle has at least 2 sides of the same length. Thus all equilateral triangles are also isosceles.
• if all of the angels are acute but lenghths are different what is that?
• its scalene
• i got my one right but it said i got it worng
• I... I think that means you got it wrong, but you don't understand. You might want to check your answer or ask someone else to explain it to you.
• um whenever i double tap a question it ameatiatily says its wrong
• dont double tap just tap and check
• Why do all sides measurements in a triangle have to equal 180
• Nice question! I think you meant to ask why all the angle measurements in a triangle add to 180 degrees. The side measurements can add up to anything.

There is a geometry proof of the fact that the angles in a triangle must add to 180 degrees.

Draw a triangle with vertices at points A, B, and C, and draw a line through vertex C that is parallel to side AB. This diagram forms three non-overlapping angles at vertex C. Two of the angles are just outside the triangle and one of the angles is angle C inside the triangle.

These three non-overlapping angles formed at vertex C clearly add to 180 degrees (because together, they form a semicircle).

Because alternate interior angles are congruent when parallel lines are cut by another line (transversal), angle A in the triangle is congruent to one of the angles at C outside the triangle, and angle B in the triangle is congruent to the other angle at C outside the triangle.

It follows from these last two statements that angles A, B, and C in the triangle add to 180 degrees.

Have a blessed, wonderful day!