Geometry (33%): [Unit Plan 2023]
Develop spatial sense.
- Analyze puzzles and games that involve spatial awareness.
- Demonstrate an understanding of Pythagorean formula by identifying right triangles and solving right triangle problems.
- Demonstrate an understanding of sine, cosine and tangent ratios in right triangles and solve problems using the ratios.
- Demonstrate an understanding of similarity in polygons.
1. Find missing sides in a Right Triangle
- Visualize the formula using Area of Squares: VIDEO
- Solve for a missing side using area of squares or Pythagorean Formula.
- Lesson 1 (Video Notes) (Answers)
2 and 3: Given Right Triangles:
- Name the sides and angles using upper and lower case letters.
- Lesson 3 (Video Notes) (Answers)
- Naming and Writing Ratios HW (HW Lesson 3) (Answer Key) (HW3 Video)
4. Ratios as Decimals
Before we start using sine, cosine and tangent to find angles or sides we will practice writing our ratios as decimals.
Before we start using sine, cosine and tangent to find angles or sides we will practice writing our ratios as decimals.
- Lesson 4 (Video Notes) (Answers)
- HW Lesson 4 (Answers)
- Rounding Decimals (video example)
Online Calculator: Desmos
5. Find the side of a Right Triangle using:
SIN (sine), COS (cosine) or TAN (tangent)
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6. Finding an Angle of a Right Triangle using: SIN (sine), COS (cosine) or TAN (tangent)
- We will label the sides of the triangle: HYP (hypotenuse), OPP (opposite the unknown angle), ADJ (adjacent to unknown angle).
- We will write the three ratios: sinA, cosA and tanA
- Choose the ratio that solves for the unknown angle. .
- Lesson 6 (Video One - Calculator Skills) (Video Two - Triangle Ratios) [Lesson Notes]
- HW Lesson 6 (Answers)
7. Putting it all together: using SIN (sine), COS (cosine) or TAN (tangent)
- We will label the sides of the triangle: HYP (hypotenuse), OPP (opposite the unknown angle), ADJ (adjacent to unknown angle).
- We will write the three ratios: SOH CAH TOA
- Lesson 7 (Video One Examples 1ab) (Video Two Examples 2ab) [Lesson Notes]
- HW Lesson 7 (Answers)
SKILL BUILDING: SOH CAH TOA
- More finding sides and angles: (Ratio Skill Building) (Answer Key)
- Skill Building 2: (Find sides/angles knowing Answer - self check)
- Skill Building 3: (Find sides/angles with Answer Key)
8. Problem Solving: Solve Right Triangle problems using Pythagoras and/or one of the ratios: SIN, COS or TAN.
- There are two angles that are used regularly in problem solving:
- Angle of Elevation: looking up from the line of sight
- Angle of Depression: looking down from the line of sight
- If you are looking up at an angle of 75 to see a person on a balcony then the person on the balcony is also looking down at you with an angle of 75.
- Lesson 8 (Video One) (Video Two) [Lesson Notes]
- Lesson 8 HW (Answers)
9. Review all the lessons.
- General Review: [Lesson 9 HW] [Answers]
Summary Assignment
- Use Lesson 9 to help guide your work.
- Geometry Summary