Grade 7 · Free math lesson

Basic Geometry

After this lesson, you will be able to name, describe, and tell apart the most common geometry shapes.

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Skills in this unit

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Standards covered:6.G.A.17.G.B.47.G.B.54.MD.C.67.G.B.66.G.A.26.G.A.47.G.A.17.G.A.28.G.A.5

Triangles: 3 Sides Always

A triangle has exactly 3 sides and 3 corners (called vertices). The 3 inside angles always add up to 180 degrees.

Example: A slice of pizza is a triangle. If two angles are 60° and 80°, the third angle must be 180 - 60 - 80 = 40°.

Remember: TRI means 3 — like tricycle has 3 wheels!

Quadrilaterals: 4 Sides

Any shape with exactly 4 sides is called a quadrilateral. Squares, rectangles, and parallelograms are all quadrilaterals — their 4 angles always add up to 360°.

Example: A rectangle has 4 right angles (each 90°). Check: 90 + 90 + 90 + 90 = 360°. ✓

Remember: QUAD means 4 — like a quad bike has 4 wheels!

Circles: No Sides, All Round

A circle has no sides or corners. Every point on the edge is the exact same distance from the center — that distance is called the radius.

Example: A pizza with a radius of 15 cm means every point on the crust is exactly 15 cm from the center. The diameter (all the way across) = 15 × 2 = 30 cm.

Remember: Radius = from centeR to edge — R for Radius, R for Ring!

Worked example

A triangle has two angles of 55° and 75°. What is the third angle? Also, what shape has 4 equal sides and 4 right angles?

  1. 1Step 1: All triangle angles add up to 180°. Write: 55 + 75 + ? = 180.
  2. 2Step 2: Add the two known angles: 55 + 75 = 130. Then subtract: 180 - 130 = 50°.
  3. 3Step 3: A shape with 4 equal sides AND 4 right angles is a special quadrilateral called a square.

Answer: The third angle is 50°. The shape described is a square.

The #1 mistake to avoid

Students forget that a square IS a rectangle (it has 4 right angles), but a rectangle is NOT always a square (sides don't have to be equal). Remember: a square is a special rectangle!

Key takeaways

  • A triangle has 3 sides and its angles always add up to 180°.
  • A quadrilateral has 4 sides and its angles always add up to 360° — squares and rectangles are both quadrilaterals.
  • A circle has no sides; the radius is the distance from the center to the edge, and the diameter is twice the radius.

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