1819 C2X §6.4

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

Which exercises should we discuss on the board?

Pythagoras in solids

This box has the shape of a cuboid.

We will call the cuboid ABCD.EFGH

The box is 6 by 12 by 6 cm.

We can use Pythagoras' Theorem to

find the lengths of line segments

inside the box, for example, the length

of line segment BH.

Pythagoras in solids

If we want to know the length of BH,

we should find a right-angled triangle

that has BH as one of the sides.

Cross section BDHF is a rectangle

with both vertex B and vertex H, so it

contains BH. And as we know, a rectangle makes

two right-angled triangles.

Pythagoras in solids

The box is 6 by 12 by 6 cm.

So we only know that HD = BF = 6 cm

We need to find the length of BD,

so we can calculate BH.

Pythagoras in solids

The box is 6 by 12 by 6 cm.

BD lies in the base of the box,so if

we sketch ABCD, we can calculate BD

Pythagoras in solids

The box is 6 by 12 by 6 cm.

BD lies in the base of the box,so if

we sketch ABCD, we can calculate BD

Pythagoras in solids

If we add the length of BD to our

previous sketch, we can calculate BH

Pythagoras in solids

If we add the length of BD to our

previous sketch, we can calculate BH

Pythagoras in solids

When using Pythagoras' theorem in solids, sketch the cross section that contains the line segment you want to know.

Often you will have to use Pythagoras' theorem in one of the faces of the solid first.

Pyramids

Cross sections in a pyramid are usually

isosceles triangles.

Pyramids

Cross sections in a pyramid are usually

isosceles triangles.

Pyramids

AS is half of AC, so

(and that is NOT          !!!)

SC=​2​​1​​√​200​​​

√​100​​​

HW Tuesday

Make and correct §6.4