Warm-Up (7 min) Full sentences Start a new page, date on top. Homework can be found on the __________ and the ____________________. Update planner now. The following tools are required every day:___ _________, ________, ________, _________. On a test, you may use your own __________. At the end of class, you are graded on ______ _______________, ___________, ___________ If you have been absent, it is your responsibility to ___________________________________.

Start a new page, date on top. Homework can be found on the back wall and the class webpage. Update planner now. The following tools are required every day: pencils, notebook, grading pen, compass, protractor. On a test, you may use your own calculator. At the end of class, you are graded on leaving floor clean, book & whiteboard in desk, chair pushed in. If you have been absent, it is your responsibility to submit late HW after school with note, and take notes from website or friend.

Ch. 9 The Pythagorean Theorem Special Right Triangles Distance in Coordinate Geometry Ch. 12 Trigonometric Ratios

Right Triangles Long side, opposite right angle

The Pythagorean Theorem c is always the hypotenuse. It does NOT matter which leg is a or b.

Find missing side x.

Find missing side y.

Find missing side x on your own. 25 x 20

Planner up-to-date? HW due & out? Date in notes? You must have a red or green pen to correct your own _____ and other people’s _________ when we go over every answer. Tutoring is available in this room ___________ and _____________ most weeks. Quizzes may be retaken after ______within _____. To improve a unit test grade, complete the necessary exercises on ____________________. Extra credit is available by _______________ and _________________________________________ Complete warm-up in notebook (7 min)

You must have a red or green pen to correct your own HW and other people’s quizzes when we go over every answer. Tutoring is available in this room Tuesday and Thursday most weeks. Quizzes may be retaken after school within one week of the original. To improve a unit test, complete the necessary exercises on Khan Academy. Extra credit is available by winning games and explaining challenging solutions to the class.

Team Activity (10 min) 1.Cut out six squares from graph paper: 3, 4, 5, another 5, 12, & 13 units per side. 2.Arrange sets of three squares, corner-touching- corner, so that they form right triangles. 3.With your team, discuss how these arrangements demonstrate the Pythagorean Theorem. 4.Draw both arrangements in your notes, label with dimensions, explain how they demonstrate the P.T. in words and equations.

Can you make a right triangle from squares with 9, 11 & 14 cm?

Pythagorean Theorem If a shape is a right triangle, then a 2 + b 2 = c 2. Converse of the Pythagorean Theorem If a 2 + b 2 = c 2, then a shape is a right triangle.

Converse of Pythagorean Theorem ? ? ≠ 196 Not a right triangle! Sides do not work with the P.T.

Pythagorean Theorem If a shape is a right triangle, then a 2 + b 2 = c 2. Converse of the Pythagorean Theorem If a 2 + b 2 = c 2, then a shape is a right triangle. Inverse of the Pythagorean Theorem If a shape is not a right triangle, then a 2 + b 2 ≠ c 2. Contrapositive of the Pythagorean Theorem If a 2 + b 2 ≠ c 2, then a shape is not a right triangle.

Any HW to put out? Planner up-to-date? Copy this… A right triangle with sides of 3 and 4 units long, always has a hypotenuse of exactly 5 units. This ratio is the same even if dilated x 2

Special Right Triangles All triangles with two congruent corresponding pairs of angles are similar. That’s the AA Triangle Similarity Shortcut.

Special Right Triangles Because the sides all grow by the same scale factor, the ratio of sides within the triangle remains the same. Some special ratios are: 1.41 ≈ 1.73 ≈

Are these right triangles? Are these special right triangles? If so, which ones? Justify your reasoning. 13 cm 15 cm 9 cm 10 cm 24 cm 26 cm

Calculate the length of this segment (4, 5) (2, 2)

1. Calculate lengths of ‘legs’ (4, 5) (2, 2) X = 4 – 2 = 2 Y = 5 – 2 = 3 Δ = change Δ = final - initial Δx = x 2 – x 1 Δy = y 2 – y 1 3 units 2 units

2. Calculate segment length with P.T. (4, 5) (2, 2) 3 units 2 units

Calculate the length of this segment

Calculate the slope of this segment

Calculate the midpoint of this segment

This is the bottom half of a segment. Calculate the upper left endpoint, and its overall length.

In Your Notebook (10 min) 1.Graph (1, 1) (2, 1) (1, 2) 2.Use rays centered on the origin and going through each vertex, dilate this triangle with a scale factor of 4. 3.Write a coordinate rule for this dilation. 4.Using your protractor, measure and label all interior angles of the pre-image and image. 5.Using a ruler, measure and label all the side lengths in both triangles.

Story Problems Handout - Right Triangle Geometry Make sure you get each question stamped. Due before end of class. For each question, each part, draw detailed pictures. Label distances with units. #1 picture & calculations at bottom. #2-4 on back.

Warm-Up (5 min) What are the missing side lengths? 1 m ? m 6 m

√3 m 3√3 m Warm-Up Answer 1 m 2 m 3 m 6 m

√3 m 3√3 m Ratios of sides stay the same when dilating or scaling up/down 1 m 2 m 3 m 6 m

Trigonometry Ratios Sine angle = __Opposite length___ Hypotenuse length Cosine angle = __Adjacent length___ Hypotenuse length Tangent angle = _Opposite length___ Adjacent length

Trigonometry Ratios Mneumonic SOH = Sine angle = __Opposite length___ Hypotenuse length CAH = Cosine angle = __Adjacent length___ Hypotenuse length TOA = Tangent angle = _Opposite length___ Adjacent length

Trigonometry Ratios Sine angle = __Opposite length___ Hypotenuse length Cosine angle = __Adjacent length_ Hypotenuse length Tangent angle = _Opposite length_ Adjacent length opposite hypotenuse adjacent angle

Find missing side lengths. Which Trigonometry Ratio to Use? 10 m 53 o

5 min Warm-Up Draw and label diagram. Find missing side lengths. Which Trigonometry Ratios to Use? 10 m 36 o Have you updated your planner today?

Draw and label diagram. Find missing angle. 3 m 2 m ? o

Trigonometry Practice Two practice worksheets each. Work with partners who have same sheet. When you complete the first worksheet, get checked off for credit. Receive second, complete, get checked off. HW due tomorrow as well. Have you updated your planner today?

Trigonometry Practice HW out for credit in first minute. Two practice worksheets each. Work with partners who have same sheet. When you complete the first worksheet, get checked off for credit. Receive second, complete, get checked off. Have you updated your planner today?

Right Triangles Review Warm-Up (5 min) 1.In a right triangle, if you know the lengths of two sides, you can calculate the third using the __________________. 2.In any right triangle, the _____ of an angle is equal to the ratio of the opposite side/hypotenuse. 3.A right triangle has a ‘leg’ of 6 and a hypotenuse of 10. Calculate the missing leg. 4.Calculate the three interior angles in the triangle in Q3?

Whack-a-Mole Review Game Teams of 3-4 at adjacent desks. All your names on answer sheet. Number answer sheet Each team starts with a few question cards. Answer these in correct place on sheet. Hold up cards to signal ‘ready-to-trade.’ One person each team makes trade. When answer all 25 Q’s, turn in sheet, return. If some wrong, will be returned. Trade for those cards and revise answers. Extra credit based on when you get all correct.

1. HW out for check. 2. Take trigonometry quiz. 3. Switch ‘n’ grade quiz. 4. Go over HW. 5. Any missing quizzes/HWs in gradebook? Complete after school today. 6.Junior SAT tomorrow. 7.Launch rocket tomorrow. Max alti?