Triangle Graphic Organizer – Classify by Sides and Angles

How it works

Every triangle has two names, one for its sides and one for its angles. This triangle graphic organizer crosses the two lists, and working out which boxes must stay empty teaches as much as filling in the rest.

Read the full guide

Triangle graphic organizers by grade

In the Common Core standards, 4th grade students draw right, acute and obtuse angles and recognize right triangles as a category. The sheet on the three angle names fits that work, and the side names can wait until the class is ready for them.

Two meanings of isosceles

Some books say an isosceles triangle has exactly two equal sides. Others say at least two, which makes every equilateral triangle isosceles as well. The blank sheets work with either meaning, so tell the class which one you use.

Mark equal sides with matching tick marks, so the drawing itself shows the name.
The largest angle alone decides the angle name, so look at it first.

Questions and answers

How are triangles classified by sides and angles?

By sides: equilateral, with all three equal, isosceles, with two equal, and scalene, with none equal. By angles: acute, with every angle under 90°, right, with one angle of 90°, and obtuse, with one angle over 90°.

Can an equilateral triangle be a right triangle?

No. All three angles of an equilateral triangle are 60°, so it is always acute. It can never be right or obtuse, which is why two boxes of the chart cannot be drawn.

Can a right triangle be isosceles?

Yes. When the two sides that form the right angle are the same length, the triangle is both right and isosceles. Its other two angles are 45° each.

Do the angles of a triangle add up to 180 degrees?

Yes. The three interior angles of any triangle drawn on a flat surface add up to 180°. That is how the third angle is found when two are known.

All 9 organizers

Sides and angles 4

Triangle graphic organizer: sides by angles Equilateral, isosceles and scalene across the top, acute, right and obtuse down the side, and a box to draw a triangle that is both. Two of the nine boxes cannot be drawn.
Triangles by angles: acute, right, obtuse Three boxes for the angle names, on a sideways page. Draw each triangle, mark its largest angle, then write what makes it acute, right or obtuse.
Triangles by sides: equilateral, isosceles, scalene Three boxes across a sideways page. Draw each triangle, mark its equal sides with small ticks, then write how to tell it from the other two.
Types of triangles chart: six names All six names down the side, with a box beside each for how to tell and a box for a sketch.

Classify 3

Always, sometimes, never: eight statements about triangles Judge each statement, then give a reason. Key: 1 and 6 are always true; 2, 5 and 7 sometimes; 3, 4 and 8 never.
Classify seven triangles from their angles The three angles of seven triangles, from 60° 60° 60° to 120° 35° 25°. Tick one name for the sides and one for the angles in every row.
Find the third angle Two angles are given in each of six rows. Work out the third, then name the triangle by its angles and by its sides. The third angles are 70°, 45°, 120°, 40°, 60° and 90°.

Sample and answer key 2

Answer key: seven triangles The tick chart with the right boxes marked. A class that counts an equilateral triangle as isosceles ticks both in the first row.
Sample triangle organizer, filled in The opening chart with all nine boxes written in, the two impossible ones among them, and the drawings left to make.