Shapes in the Plane
Primary 4 · Mathematics
Shapes in the Plane
Lesson 3 of 5
25 min
Let's begin
During umuganda, Mugisha's family marks out a new vegetable garden with four sticks and a rope. The rope makes a shape with four straight sides. "What do we call this shape?" asks his little sister.
A shape with four straight sides is a quadrilateral. Today you will learn the names of its parts.
"Quad" means four. A quadrilateral is a closed shape with 4 straight sides, 4 vertices and 4 angles. Your exercise book, a window and a football pitch are quadrilaterals.
We name it by its vertices, going round in order: quadrilateral ABCD. The sides are AB, BC, CD and DA.
A diagonal is a line segment that joins two opposite vertices. Every quadrilateral has 2 diagonals. In ABCD they are AC and BD.
A diagonal cuts a quadrilateral into 2 triangles. Each triangle's angles add up to 180°, so the quadrilateral's angles add up to 2 × 180° = 360°.
Example: three angles of a quadrilateral are 80°, 100° and 90°. They make 270°. The fourth angle is 360 − 270 = 90°.
Tip
Adjacent = next door, opposite = across the road. A diagonal is a short cut across the garden from one corner to the far corner.
Work each one in your exercise book first. Then tap Show answer to check.
How many sides, vertices and angles does a quadrilateral have?
Answer: 4 sides, 4 vertices and 4 angles.
In quadrilateral PQRS, which side is opposite PQ?
Answer: RS (you can also say SR).
In quadrilateral PQRS, name the two diagonals.
Answer: PR and QS.
Three angles of a quadrilateral are 90°, 90° and 90°. What is the fourth?
Answer: 90°, because 360 − 270 = 90.
A diagonal cuts a quadrilateral into how many triangles?
Answer: 2 triangles.
What you learned today
Sources and credits
The diagonals and the 360° angle sum were written by Ganzaa. The stories, Rwandan examples, diagrams and practice questions were written by Ganzaa.
Quick check
In quadrilateral WXYZ, which side is opposite WX?
