Shapes in the Plane
Primary 4 · Mathematics
Shapes in the Plane
Lesson 2 of 5
25 min
Let's begin
Byiringiro folds a square piece of paper along its diagonal to make a triangle. "One corner is still a square corner!" he notices. His friend folds a long thin triangle with a very wide corner.
We can also sort triangles by their angles. You already know acute, right and obtuse angles, so you are ready.
Try this! Cut out any paper triangle. Colour its three corners, tear them off and fit them together at one point. They always make a straight line, which is 180°.
So if you know two angles, you can find the third. Example: a triangle has angles of 70° and 50°. They make 70 + 50 = 120°. The third angle is 180 − 120 = 60°.
Two right angles already make 90 + 90 = 180°. There would be nothing left for the third angle! In the same way, a triangle can have at most one right angle or obtuse angle. The other two angles are always acute.
Byiringiro's folded square gives a triangle with a right angle and two equal sides. It is a right-angled isosceles triangle.
Tip
Look for the biggest angle. Is it less than 90°? Acute-angled. Exactly 90°? Right-angled. More than 90°? Obtuse-angled. And all three angles always share 180°.
Work each one in your exercise book first. Then tap Show answer to check.
A triangle has angles 60°, 60° and 60°. Name it by its angles.
Answer: Acute-angled. Every angle is less than 90°.
A triangle has angles 90°, 45° and 45°. Name it by its angles.
Answer: Right-angled.
Two angles of a triangle are 40° and 30°. Find the third angle.
Answer: 110°, because 180 − 40 − 30 = 110. The triangle is obtuse-angled.
Can a triangle have angles of 100° and 95°? Explain.
Answer: No. 100 + 95 = 195, which is already more than 180°.
A right-angled triangle has one angle of 35°. Find the third angle.
Answer: 55°, because 180 − 90 − 35 = 55.
What you learned today
Sources and credits
The angle-sum activity (tearing off the corners) and its diagram were written by Ganzaa. The stories, Rwandan examples, diagrams and practice questions were written by Ganzaa.
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