## MATHEMATICS 10-3

[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation

[PS] Problem Solving
[R] Reasoning
[T] Technology
[V] Visualization

### Geometry

General Outcome: Develop algebraic and graphical reasoning through the study of relations.

Specific Outcomes: It is expected that students will:

1. Demonstrate an understanding of similarity of convex polygons, including regular and irregular polygons.
[C, CN, PS, V]

3.1 Determine, using angle measurements, if two or more regular or irregular polygons are similar.

## Similar and/or Congruent - congruent not part of the program of studies, but perhaps important enough to include - iFrame

3.2 Determine, using ratios of side lengths, if two or more regular or irregular polygons are similar.

3.3 Explain why two given polygons are not similar.

3.4 Explain the relationships between the corresponding sides of two polygons that have corresponding angles of equal measure.

3.5 Draw a polygon that is similar to a given polygon.

3.6 Explain why two or more right triangles with a shared acute angle are similar.

3.7 Solve a contextual problem that involves similarity of polygons.

1. Demonstrate an understanding of primary trigonometric ratios (sine, cosine, tangent) by:
• applying similarity to right triangles
• generalizing patterns from similar right triangles
• applying the primary trigonometric ratios
• solving problems.
[CN, PS, R, T, V]
[ICT: C6–4.1]

4.1 Show, for a specified acute angle in a set of similar right triangles, that the ratios of the length of the side opposite to the length of the side adjacent are equal, and generalize a formula for the tangent ratio.

## Naming Sides of a Right Triangle

4.2 Show, for a specified acute angle in a set of similar right triangles, that the ratios of the length of the side opposite to the length of the hypotenuse are equal, and generalize a formula for the sine ratio.

## Sine - Math Glossary - Under Construction - Consider showing reference angle and side lengths. Display opp/hyp ratio.

4.3 Show, for a specified acute angle in a set of similar right triangles, that the ratios of the length of the side adjacent to the length of the hypotenuse are equal, and generalize a formula for the cosine ratio.

## Cosine - Math Glossary - Under Construction - Consider showing reference angle and side lengths. Display adj/hyp ratio.

4.4 Identify situations where the trigonometric ratios are used for indirect measurement of angles and lengths.

4.5 Solve a contextual problem that involves right triangles, using the primary trigonometric ratios.