Geometry
Understanding elementary shapes
Classify angles by size, triangles by their sides and their angles, and tell flat shapes from solid ones.
Angles are measured by how far something turns, in degrees. A full turn is 360°, so a quarter turn is 90° — the right angle you see at the corner of a page. Every other angle is named by where it sits against those two landmarks.
The five names for an angle
Acute: less than 90°. Right: exactly 90°. Obtuse: more than 90° but less than 180°. Straight: exactly 180°, a half turn. Reflex: more than 180° but less than 360°. A full turn of 360° gets its own name, a complete angle. Every angle between those sizes has exactly one of these names, decided only by its size.
Two ways to name a triangle
By its sides: equilateral has three equal sides, isosceles has two, scalene has none. By its angles: acute-angled has three angles under 90°, right-angled has one of exactly 90°, obtuse-angled has one over 90°. Every triangle has one name of each kind, because the two questions are different questions.
Have a play
Four angles, drawn side by side and getting wider as you go. Find out what each one is called.
Tap any part of the picture.
Worked example
Name the triangle with two angles of 40° and one of 100°, where the two sides facing the 40° angles are equal.
By sides: exactly two are equal, so it is isosceles.
Isosceles means exactly two equal sides — and where two sides are equal, the two angles facing them are equal too, which is why 40° appears twice. Check: 40 + 40 + 100 = 180, so the triangle really can exist.
Try it together
Now let us describe the triangle whose angles are 40°, 40° and 100°.
Check the angles first, then name the triangle both ways.
1.The angles of any triangle add up to 180°. What is 40 + 40 + 100?
Have a go
Have a go on your own: two angles of a triangle are 30° and 70°. How big is the third, in degrees?
Hint: The three angles have to add up to 180°.
Ready to practice?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.