# 2TTO §6.5 Right, acute or obtuse 20-21

Which exercises should we discuss on the board?
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Slide 1: Mind map
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This lesson contains 11 slides, with interactive quiz and text slides. Lesson duration is: 50 min

## Items in this lesson

Which exercises should we discuss on the board?

#### Slide 1 -Mind map

Right-, Acute- and Obtuse-angled triangles
We've learned that Pythagoras' theorem only works in right-angled triangles: the squares on the short sides are added up the same as the square on the hypotenuse.

That means if the squares on the short sides are NOT added up the square on the hypotenuse, we do NOT have a right-angled triangle.

#### Slide 2 -Slide

Right-, Acute- and Obtuse-angled triangles
What happens to the hypotenuse when we change the right angle?

#### Slide 3 -Slide

Right-, Acute- and Obtuse-angled triangles
hypotenuse larger        hypotenuse smaller
= larger angle                  = smaller angle

#### Slide 4 -Slide

Right-, Acute- and Obtuse-angled triangles
A triangle with one angle that is larger than 90
degrees is called an obtuse-angled triangle.

A triangle where all angles are smaller than 90
degrees is called an acute-angled triangle.

#### Slide 5 -Slide

Right-, Acute- and Obtuse-angled triangles
When you are given a triangle with 3 known sides. You can use Pythagoras' theorem to calculate if it is a right-angled, acute-angled or obtuse-angled triangle.
1) Sketch the triangle
2) Use the two shorter sides to calculate the hypotenuse as if it was a right-angled triangle
3) Compare the results:
If the given third side is the same as the calculated hypotenuse, you have a right-angled triangle.
If the given third side is larger than the calculated hypotenuse, you have an obtuse-angled triangle.
If the given third side is smaller than the calculated hypotenuse, you have an acute-angled triangle.

#### Slide 7 -Slide

Right-, Acute- and Obtuse-angled triangles
In triangle PQR, PQ = 6, QR = 11 and PR = 9.
What type of triangle is triangle PQR?
1) Sketch:

#### Slide 8 -Slide

Right-, Acute- and Obtuse-angled triangles
In triangle PQR, PQ = 6, QR = 11 and PR = 9.
What type of triangle is triangle PQR?
1) Sketch:

#### Slide 9 -Slide

Right-, Acute- and Obtuse-angled triangles
In triangle PQR, PQ = 6, QR = 11 and PR = 9.     2) Calculation:
3) Conclusion:

QR is longer than what I
calculated. Therefore the
angle is larger than 90
degrees. PQR is an
obtuse-angled triangle.

What type of triangle is triangle PQR?
1) Sketch:

#### Slide 10 -Slide

Homework

Make T2, T5 and E8 a and b