We study similar triangles, which have the same shape, but not the size. When two triangles are similar, their corresponding angles are the same, and their corresponding sides are proportional. The constant ratio is called the scale factor.

Two triangles ABC and XYZ, they are similar if:

• Angle X = Angle A, and Angle Y = Angle B (which implies that Angle Z = Angle C. This is AAA) or
• XY / AB = YZ / BC = ZX / CA   (This is three sides are proportional. SSS) or
• XY/AB = ZX / CA ,and Angle X = Angle A  (this is two sides with including angle. SAS)

We can use the above three rules to decide if two triangles are similar.

We now start Chapter 9 on Mensuration, about measurement.

We first study sectors in a circle, the arcs. For a sector facing an angle X, we have the following:

Length of arc / circle circumference = X / 360  and Area of sector / Area of the circle = X / 360

From the above, we can further derive the relationship between the length of the arc (say a) with the area of the sector (say A) on a circle with the radius r as:

A = ar / 2

We then study the volumes and surface areas of a cone and a pyramid where both volume has the formulae of:

V = (1/3) * Base Area * Height

Armed with the formula for sectors/arcs, we can calculate the surface are for a cone.

Below is this week’s homework:

Page 84, # 8 – #22

Page 89, #3 – #5, #8, #10, #41, #45, #48, #51, #58, #60