Geometry
Unit Plan: Schedule, Quiz and Exam Dates
2023 Assessments:
- Demonstrate and understanding of angles and parallel lines.
- Solve right triangles using: sine, cosine, tangent and/or Pythagorean Theorem
- Solve triangles using: Law of Sines and/or Law of Cosines
Unit Plan: Schedule, Quiz and Exam Dates
2023 Assessments:
Right Triangle Review
Cosine = adjacent/hypotenuse
Tangent=opposite/adjacent
We can find missing sides and/or missing angles in right triangles using these ratios.
Lesson: Warmup (Skills Review) Original and Answer Key
Practice: HW and Answer Key
- Find sides using Pythagorean Theorem (a^2+b^2=c^2)
- Basic Trig Ratios:
Cosine = adjacent/hypotenuse
Tangent=opposite/adjacent
We can find missing sides and/or missing angles in right triangles using these ratios.
Lesson: Warmup (Skills Review) Original and Answer Key
Practice: HW and Answer Key
- Extra Practice Questions - worksheet on solving triangle (find all the missing information). Original and Answer Key
Intro to Law of Sines and Law of Cosines.
Law of Sines
Can be used to find angles and sides in any triangle where we know an angle and its side opposite:
Substitute the information we know from the triangle and solve for the missing sides or angles.
Law of Cosines
When we are not able to use the Law of Sines we can always use the law of cosines.
Use the Law of Cosines to find a side when given 2 sides and the included angle.
When we are not able to use the Law of Sines we can always use the law of cosines.
Use the Law of Cosines to find a side when given 2 sides and the included angle.
Use the Law of Cosines to find an angle when given all 3 sides.
Lesson:
Skill Building
Skill Building 1:
Skill Building 2
- Use the given triangle properties to determine which formula can be used to solve for the unknown side and/or the unknown angle.
Skill Building 1:
- Continue: Law of Sines or Law of Cosines.
- Geometry Skills: Sine and Cosine Practice (old quiz 2017) and Answer Key
Skill Building 2
- Original and Answer Key
Skill Building 3
Law of Sines or Law of Cosines? Original
Triangle Flow Chart - what to use?
Problem Solving:
Given information draw and label a triangle; solve for the unknown value(s).
Lesson: Text Questions: [Textbook Pages]
Page 139 - 3,4, 6ab, 10 and 13 [Text Examples]
Page 151 - 4, 5, 7ab, 8, 13
Problem Solving - review (text questions 4 and 13)
Parallel Lines and a Transversal:
Parallel Lines: Lesson
Parallel Lines & angle properties; equations and solving.
Triangle Properties.
Assessment:
Building Skills. Do 3 or 4 of the following:
Regular Polygons.
General Review
2022 Geometry Exams
Review to Remember, Remember to Review:
- Trigonometry Quiz 2020: Original and Answer Key
Law of Sines or Law of Cosines? Original
- What to use: Law of Sines or Law of Cosines
- Full Solutions: Show the Work
Triangle Flow Chart - what to use?
Problem Solving:
Given information draw and label a triangle; solve for the unknown value(s).
Lesson: Text Questions: [Textbook Pages]
Page 139 - 3,4, 6ab, 10 and 13 [Text Examples]
Page 151 - 4, 5, 7ab, 8, 13
Problem Solving - review (text questions 4 and 13)
Parallel Lines and a Transversal:
- Several pairs of angles have the same measure when parallel lines are crossed by a transversal line: corresponding angles, alternate interior angles and alternate exterior angles.
- Corresponding Angles: same side of transversal and same side of parallel lines (above and right, below and left, etc.)
- Alternate Interior Angles: between the parallel lines and opposite sides of the transversal
- Alternate Exterior Angles: outside the parallel lines and opposite sides of the transversal
- Same Side Interior Angles are supplementary (add to 180)
- When we have intersecting lines, each pair of Opposite Angles are equal to each other.
Parallel Lines: Lesson
- Picture of Poster
- Notes and Examples: September 2020
Parallel Lines & angle properties; equations and solving.
- Practice: original and answer key
- Video: Questions 1 - 5
Triangle Properties.
- We combine these 3 thoughts to solve angle problems in triangles:
- All the angles in a triangle add up to 180.
- A straight line has an angle measure of 180.
- Properties of a transversal and parallel lines.
- Lesson: Solve using properties of triangles and parallel lines
- Notes and Examples: September 2020
Assessment:
- Problems: given triangle properties and word problems
- Triangles: properties and skill building.
- Polygons, Triangles and Angles
Building Skills. Do 3 or 4 of the following:
- Name type of angle pair, their property, solve: Original and Answer Key
- Angles in Triangles Skills: Original and Answer Key
- Angle Skill Building (Old Quiz 2019): Original and Answer Key
- Parallel Lines & Angles in Triangles (write angle properties, write an equation for the properties, solve): Original and Answer Key
Regular Polygons.
- We can determine the total sum of angles in convex polygons by counting the number of triangles, less 360 from the centre angle created by all the triangles.
- If the polygon is 'regular' all the interior angles are the same size. We can divide the angle sum by the number sides to determine how large each angle is.
- Lesson: Regular Polygons Notes
- Notes and Examples: September 2020
- Build Skills: Regular Polygons and Answer Key
General Review
- Skill Builders: Original and Answer Key
- REVIEW 2: Original and Answer Key
2022 Geometry Exams
Review to Remember, Remember to Review: