This checkpoint is split into two parts: Part 1 is about shapes and Part 2 covers Pythagoras Theorem. While Pythagoras Theorem is part of trigonometry (covered in the next checkpoint), it is useful to learn as an introduction as it commonly tested for questions concerning geometry.

PART 1 - Shapes

You need to know how to calculate perimeter and also area for various shapes. Let's go through them.

Aside from that, you also need to know the various types of 3D shapes around:

ANGLES

The most important thing to note with angles is to see them as a PART OF A WHOLE = 360 DEGREES for 4 SIDED SHAPES and CIRCLES and 180 DEGREES for TRIANGLES.

Let's look at types of angels (what the video and make notes) and what they look like.

• RIGHT ANGLE – lines that intersect are perpendicular.
• STRAIGHT ANGLE – Angles forming straight lines add up to 180 degrees (2 sides of the straight line add to 360!).
• ANGLES around a point add up to 360 degrees.
• ANGLES in a SQUARE add up to 360.
• ANGLES in a TRIANGLE add up to 180.

Parallel Lines

When parallel lines are crossed:

• Corresponding angles are equal (for examples, a = e).
• Alternate interior angles are equal (d = f).
• Same side interior angles add to 180 if on a straight line.

Now, let's go through some questions:

Q33

I am a 3D solid with 6 equal faces

Which shape am I?

A rectangular solid B cube C Cone D cylinder

What is the area, in square units of a square that has the same perimeter as the rectangle above?

A 16 B 32 C 36 D 64

In the figure below what is the value of x?

A 25 B 45 C 30 D 90

What is the area of the frame in the figure below if the inside picture has a length of 10 and a width of 6?

PART 2 – Pythagoras' Theorem

Helps you to find 1 side if you have the 2 other sides with a formula. Applies only to:

• RIGHT ANGLED TRIANGLES

Here's the formula:

Here's how they came up with it:

As an addition to Pythagoras theorem, we have SOH CAH TOA:

Now let's go through some extension questions:

Q25

The square box has dimensions as shown. What is the length of the line AH?

A 12√3 B 13√2 C 5√6 D 6√5 E None of these

Q52 - The correct ratio to find x is

A 18 sin 75⁰ B 18 sin 15⁰ C 16 sin 15⁰ D 16 sin 75⁰ E 15° cos 16

Q59 - x = ?

A 6 B 9 C -6 D -16 E None of these

Now it's time to do your assignment.

1. Download the assignment questions here.
2. Print it out or if you want to do it electronically, save it.
3. Complete the questions to it.
4. Then check the solutions on the video below. The answer key is also on the final page of your downloaded assignment questions.

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