We study transformations. A transformation, also known as a mapping, transforms a figure into another figure. Today we focus on refection, rotation, and translation.

Reflection, like a mirror, maps an image along a reflection line, into a mirrored image. Rotation rotates an image along a fixed point for certain degree into another image. And translation moves an image in certain direction (note, there is no turning).

In all three transformations above, they maintain the following: segments to equal segments; angles to equal angles, whole figures to equal whole figures.

We talk about how to calculate coordinates in a coordinate system for simple reflection, rotation, and translation.

Homework:

Page 114, 1, 2, 3, 4, 6a, 6b, 9, 10, 11, 12a

We cover the solution sof right-angled triangles with sin, cos, tan applications and how to apply them to solve simple real world problems.

Just want to point out for parents, our teaching about trigonometry is very basic, we are not going to go more than what we have taught so far.

Homework:

Page 108, #9, #11, #18, #19, #24, #26, #28, #31, #32, #33, #38

Pythagorean Theorem is the first topic we cover for this lesson. For a right-angled triangle with two sides a and b and a hypotenuse c, then we have c^2 = a^2 + b^2.

We show two ways of proving this, and we also show how to prove the reverse, that is, if a triangle with 3 sides as a, b, and c, and c^2 = a^2 + b^2, then it is a right-angled triangle with c as its hypotenuse.

With this theorem, not only can we solve some questions related to right-angle triangles, but also some real world scenarios.

We talk about indirect measure with Angle of elevation and Angle of depression. Furthermore, we study the trigonometrical ratios and give the definition of sine, cosine, and tangent and how to use a calculator to get the value of the ratio from an angle,. and from a value back to an angle.

Homework:

Page 107, #1, #2, #3, #5, #6, #8. #10. #12, #34, #36, #37.