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

• Wiskunde
• Middelbare school
• havo, vwo
• Leerjaar 2

Which exercises should we discuss on the board?

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.

Right-, Acute- and Obtuse-angled triangles

What happens to the hypotenuse when we change the right angle?

Right-, Acute- and Obtuse-angled triangles

                                            hypotenuse larger        hypotenuse smaller

                                            = larger angle                  = smaller angle

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.

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.

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:                      

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:                      

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:                      

Homework

Make T2, T5 and E8 a and b