Quarter 2, Week 8: December 4th – 8th

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Teacher Felicia Taylor Geometry Honors 8th 17th 4: Right Triangles and Trigonometry
Standard(s) Taught

MAFS.912.G-SRT.2.4

Prove theorems about triangles.  (Theorems include: the Pythagorean Theorem proved using triangle similarity.)

MAFS.912.G-SRT.3.6

Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

MAFS.912.G-SRT.3.7

Explain and use the relationship between the sine and cosine of complementary angles.

MAFS.912.G-SRT.3.8

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Learning Targets and Learning Criteria

I can:

define geometric mean.
find measures in similar right triangles using geometric mean.
apply theorems, postulates, or definitions to prove theorems about triangles, including proving The Pythagorean Theorem using triangle similarity.

demonstrate that within a right triangle, line segments parallel to a leg create similar triangles by angle-angle similarity.
use characteristics of similar figures to justify the trigonometric ratios.
define the following trigonometric ratios for acute angles in a right triangle: sine, cosine, and tangent

.• calculate sine and cosine ratios for acute angles in a right triangle when given two side lengths.
use a diagram of a right triangle to explain that for a pair of complementary angles A and B, the sine of angle A is equal to the cosine of angle B and the cosine of angle A is equal to the sine of angle B.

use Special Right Triangles (30°-60°-90° and 45°-45°-90°) to solve for missing side lengths.
use angle measures to estimate side lengths and vice versa.
solve right triangles by finding the measures of all sides and angles in the triangles using Pythagorean Theorem and/or trigonometric ratios and their inverses.
draw right triangles that describe real world problems and label the sides and angles with their given measures.
solve application problems involving right triangles, including angle of elevation and depression, navigation, and surveying.
draw an altitude to create two right triangles and can establish the relationships of the sides in each right triangle using the sine and cosine functions of a single angle in the original triangle.
• represent real world problems with diagrams of right and non-right triangles and use them to solve for unknown side lengths and angle measures.

Classroom Activities

Monday (2nd Period) / Tuesday (7th & 8th Periods)

• Bellringer – Proving Theorems about Triangles – Part 4 – Standard MAFS.912.G-SRT.2.4
• Instruction – Trigonometry – Part 1 – Standard MAFS.912.G-SRT.3.6 & MAFS.912.G-SRT.3.7
• Homework – Trigonometry Worksheets (ODD PROBLEMS ONLY) – due Thursday, December 7th for 2nd Period / due Friday, December 8th for 7th & 8th Periods

Wednesday (All Classes)

• Bellringer – Right Triangles Similarity – Part 1 – Standard MAFS.912.G-SRT.2.4
• Instruction – Trigonometry – Part 2 – Standard MAFS.912.G-SRT.3.6, MAFS.912.G-SRT.3.7 & MAFS.912.G-SRT.3.8
• Homework – IXL – R.4 Trigonometric functions of complementary angles – due Monday, December 11th for 2nd Period / due Tuesday, December 12th for 7th & 8th Periods

Thursday (2nd Period) / Friday (7th & 8th Periods)

• Bellringer – Right Triangles Similarity – Part 2 – Standard MAFS.912.G-SRT.2.4
• Instruction – Angles of Elevation and Depression – Standard MAFS.912.G-SRT.3.8
• Homework – Angles of Elevation and Depression Worksheets – due Wednesday, December 13th for all students
Assignments Due

Summative

None – However, the RETAKE – Unit 2B/3 Test is due this week by Friday, December 8th – for those who desire to retake the Unit 2B/3 test.  The re-take is available on MathSpace.

Formative

Worksheets (ONLY DO THE ODD PROBLEMS)

1.  Pythagorean Theorem Worksheets – due Monday, December 4th for 2nd Period / due Tuesday, December 5th for 7th & 8th Periods
2. Special Right Triangles Worksheets – due Wednesday, December 6th for all students
3. Trigonometry Worksheets – due Thursday, December 7th for 2nd Period / due Friday, December 8th for 7th & 8th Periods