1718 WB1Z CH11 Lesson 4

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 1

Which exercises/theory should I discuss on the board?

Sum of the angles

The sum of the three angles in a triangle is 180°
The sum of the four angles in a quadrilateral is 360°

∠A+∠B+∠C=180°

∠D+∠E+∠F+∠G=360°

Why is the sum of the angles in a triangle 180°?

You can watch the proof here:
https://www.khanacademy.org/math/basic-geo/basic-geometry-shapes/triangle-angles/v/proof-sum-of-measures-of-angles-in-a-triangle-are-180
(You do not have to know the proof)
(Khan Academy also has lots of interactive practice exercises!)

Calculating angles

You can use the sum of the angles and your knowledge of special triangles and quadrilaterals to calculate unknown angles.

Calculating angles

Calculate the size of angle C.

What size is angle C?

1. ∠C=360−82−60=218°
2. ∠C=82+60=142°
3. ∠C=180−82−60=38°
4. ∠C=​3​​(82+60)​​=37°

Calculating angles

The angle sum of a triangle is 180°

∠C=180−82−60=38°

Calculating angles

Quadrilateral DEFG is a rhombus.
Calculate the size of angle G.

What size is angle G?

1. ∠G=245°
2. ∠G=115°
3. ∠G=65°
4. ∠G=57.5°

Calculating angles

Quadrilateral DEFG is a rhombus
The angle sum of a quadrilateral is 360°
A rhombus has rotation and reflection symmetry, therefore the opposite angles are equal.

∠D=∠F=115°

∠G=∠E=​2​​(360−115−115)​​=​2​​130​​=65°

Equal angles in triangle and quadrilaterals

Isosceles triangle: 2 angles (base angles) are the same size
Equilateral triangle: all 3 angles are the same size (60°)
Rhombus/Parallelogram: opposite angles are equal
Kite: 2 angles are the same size (on either side of the axis of symmetry)
Square/Rectangle: all 4 angles are the same size (90°)

Homework Tuesday

Make and correct from §11.4:
23, 24, 25, 26, 27, 28