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Triangles and Trigonometry: Types, and Elementary Details

Can you tell an isosceles triangle from an equilateral triangle?

A scalene triangle from a right-angled triangle?

Do you remember trigonometry and Pythagoras’ theorem?

Triangles and trigonometry are important elements of the math curriculum right through school. Knowledge of triangles is applied in other aspects of STEM education (Science, Technology, Engineering, and Math) so it’s important to not get left behind.

If you or your child are baffled by triangles, then we’re here to help. This article will:

  • Explain the different types of triangles and the vocabulary used in school.
  • Give you an overview of what your child might be taught about triangles from five through to 16. 
  • Give you some ideas on how to help your child with triangles at home.

The different Types of Triangles

A triangle is a three-sided shape; almost everyone knows that. It is also always a closed and flat, 2-dimensional shape. A triangle is never 3D. There are many different 3D shapes that have triangular sides but they are not triangles.

Where it gets more complicated is when classifying the different types of triangles. Triangles are named for the features of their sides and the interior angles at each corner. Here’s a quick guide.

Equilateral triangles 

This triangle has three sides of equal length and three equal interior angles of 60° at each corner.

Isosceles triangles

An isosceles triangle has equal interior angles at two corners and two equal-length sides. 

Scalene triangles 

A triangle is scalene if there are no equal sides or angles. 

Right-angled triangles

A right-angled triangle includes one corner with an angle of 90°. There are two subtypes of right-angled triangles.

An “isosceles right-angled triangle” has one right angle and two other equal interior angles that measure 45°. The two sides that meet at the right angle are equal in length.

A “scalene” right-angled triangle has one right angle and two other interior angles that do not match. All the sides are of different lengths.

Vocabulary for talking about triangles

Lots of parents feel a bit rusty when it comes to the vocabulary of triangles. You probably learned this at school since but if you’ve not used it since, here’s a reminder.

Right-angles

A right-angle is always 90°. 

Obtuse angles

An obtuse angle is an angle greater than 90°. Both scalene and isosceles triangles can have obtuse angles. 

Acute angles

Acute angles are those less than 90°. All triangles have at least two acute angles and often all three angles are acute.

Congruent triangles

These are two triangles identical in size and shape.

Hypotenuse

The longest side of a right-angled triangle.

Pythagoras’ Theorem

This rule states, The square on the hypotenuse is equal to the sum of the squares on the other two sides.” It can be used to calculate the unknown side of a right-angled triangle.

Trigonometry

Trigonometry is used to study the relationship between the angles and sides of a right-angled triangle. The basic ratios used in trigonometry are sine, cosine, and tangent (sin, cos, and tan).

How are Triangles Taught in School?

It is always helpful to know what your child is being taught in school. This is so you can understand knowledge expectations and know what vocabulary your child might need to use. Clearly, curriculums do vary across the world and from school to school, so the explanation below is an approximation, largely based on the English National Curriculum.

Ages 5-7

Children are taught to recognize and describe a variety of basic 2D shapes like rectangles, squares, and triangles. While they need to know that triangles can appear to be quite different, they don’t need to explain the different types. The basic requirement is just to know and be able to explain that a triangle always has 3 sides and 3 corners.

Ages 7-9

Children extend their knowledge by learning about right angles. Before age 9, children will probably learn about acute and obtuse angles and the four different types of triangles described above. They can also apply their knowledge of measurement by measuring the sides of triangles.

Ages 9-11

Now pupils learn about measuring angles with a protractor and the unit of °. They combine this new skill with the vocabulary previously learned to describe and compare triangles. They will also learn that the internal angles of a triangle total 180°.

Once this is mastered, they can begin to draw triangles from given angles and lengths of sides. They should also be able to calculate an unknown angle in a triangle when the other two are given. They may also learn how to express this algebraically, such as a= 180-(b+c).

Ages 11-14

Children develop fluency in terms of measuring and describing the properties of all triangles and using a ruler and protractor to draw them. They learn the conventions of labeling the sides and angles of 2D shapes.

They then deepen their knowledge by learning how to calculate the perimeter and area of triangles. Further to this, they look at the rules for proving two triangles are congruent without measuring all sides and angles. They also learn to draw triangles in reflection and rotation.

Ages 14-16

Children now learn about Pythagoras’ Theorem and the trigonometric ratios sine, cosine, and tangent (sin, cos, tan). They’ll use these to find angles and lengths in triangles.

How to help your child with triangles and trigonometry

There are lots of fun ways of helping younger children with triangles. While you are out and about, you can spot triangles on signs and posters. Stop and count the sides and corners. You could try making collage art with triangles cut from paper or wooden 2D shapes. Or build triangles from sticks. 

As your child gets older, you can help them by discussing their work on triangles and encouraging them to use the vocabulary they have learned in school. Make sure they have the right equipment at home and in school for their work on triangles and trigonometry, such as a ruler, protractor, and calculator.

Do you feel that your child is struggling with an aspect of shape or trigonometry work, or do you feel that they would benefit from being extended or challenged?

Then consider enrolling them in math classes for kids.

Triangles and trigonometry are very important areas of math. It’s crucial to get an excellent understanding before moving onto more advanced studies post-16 and beyond, especially if your child is looking to major in a STEM subject at college or pursue a career in this area.

Yousaf Saeed (Scholarship Winner)

It is our pleasure to have Yousaf Saeed on our Guest Authors list. He is a top educationist and renowned research with major publications in his field of interest. Yousaf won a total of 3 fully-funded scholarships to complete his academic career and also won numerous fundings for attending international academic conferences. He is known for his mentorship for helping students to find and apply for international academic opportunities.

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