###### Miriam Bugeja

###### April 20, 2020

###### 1:49 pm

### This Lesson Was Contributed By:

Mathematics Department

### This Lesson is For:

### Lesson Duration:

160 mins.

#### What Should You Expect From This Lesson?

At the end of this lesson you will be able to: [1] Understand a proof that the angle sum of a triangle is 180°; [2] Understand a proof that the exterior angle of a triangle is equal to the sum of the interior angles at the other two vertices; [3] Solve problems involving the angles of triangles; [4] Understand a proof that the angle sum of a quadrilateral is 360°; [5] Understand and use properties of the quadrilaterals to solve problems involving angles.

#### How To Carry Out This Lesson At Home:

**Lesson [1] Understand a proof that the angle sum of a triangle is 180°**

**Watch the following video:**

Proof of sum of interior angles of a triangle – https://www.youtube.com/watch?v=g3zoeaDhjT8&feature=youtu.be

**Lesson [2] Understand a proof that the exterior angle of a triangle is equal to the sum of the interior angles at the other two vertices**

**Watch the following videos:**

1. Exterior Angle Theorem Proof – https://www.youtube.com/watch?v=cAk5FrQbgOY

2. What is the Relation of an Exterior Angle of a Triangle with its Interior Angles? – https://www.youtube.com/watch?v=EZ6dOlRQDBo

**Suggested Practice:**

Angles in Triangles and Quadrilateral Worksheet Pack – Worksheet 1 (documents attached in the Resources Section)

Check your answers (document attached in the Resources Section)

**Lesson [3] Solve problems involving the angles of triangles**

**Watch the following videos:**

1. Solving problems involving angles in a triangle – https://www.youtube.com/watch?v=bp5UxYKPie8

2. Solving problems involving angles in an isosceles triangle – https://www.youtube.com/watch?v=pj5k78rYtvw

3. Harder problems for angles in a triangle – https://www.youtube.com/watch?v=OdFcU37KqZY; https://www.youtube.com/watch?v=q8kXXv4o9v0; https://www.youtube.com/watch?v=RJNgoD2zrPY

**Suggested Practice:**

SMP Interact Intermediate, Student Book pg 385 ex C nos C1, C2, C3

**Lesson [4] Understand a proof that the angle sum of a quadrilateral is 360°**

**Watch the following video:**

Proof of sum of angles of a quadrilateral –https://www.youtube.com/watch?v=O94fwp1E6Lg

**Suggested Practice:**

SMP Interact Intermediate, Student Book pg 396 ex D no D1

Angles in Triangles and Quadrilateral Worksheet Pack – Worksheet 2 (documents attached in the Resources Section)

Check your answers (document attached in the Resources Section)

**Lesson [5] Understand and use the properties of the square, rectangle, parallelogram, trapezium, rhombus and kite to solve problems involving angles**

**Watch the following videos:**

1. Introduction to quadrilaterals – https://www.youtube.com/watch?v=H-ykHosJW9c

2. Properties of Quadrilaterals – https://www.youtube.com/watch?v=_-_aETcYWXk

3. Finding unknown angles in a trapezium – https://www.youtube.com/watch?v=-jRAytbVyTE

4. Finding unknown angles in a parallelogram – https://www.youtube.com/watch?v=yhMgb_wSnEI

5. Finding unknown angles in a kite – https://www.youtube.com/watch?v=OwZgEGZJCJ4

6. Finding unknown angles in a rhombus – https://www.youtube.com/watch?v=Gjn7VUMLbng

**Suggested Practice:**

SMP Interact Intermediate, Student Book pg 396 ex D nos D2

Angles in Triangles and Quadrilateral Worksheet Pack – Worksheet 3 (documents attached in the Resources Section)

Check your answers (document attached in the Resources Section)

**Acknowledgements:** Gozo College Middle and Secondary School