Trigonometry: Part 1 Similarity ReviewMenu Last semester, we spent a lot of time with similar shapes. We use the word similar to describe two figures that are the same shape, but different sizes. Two triangles are similar if the corresponding angles have the same measures.

Trigonometry: Part 1 Similarity ReviewMenu This is an example of a problem where we used the similarity to find missing measurements. The real car is 48 inches high and 176 inches long. The toy car is 3 inches high. How long is it? Real Car Toy Car Height Length X 11 inches long.

Trigonometry: Part 1 Similarity ReviewMenu On page 1 of your note packet is a sample similarity problem. Solve for x, y & z, then find the scale factor. Hints: Set up a proportion and cross-multiply to find x and z. Y is an angle, the angles should be the same in both triangles The scale factor is “how many times bigger or smaller” one triangle is compared to the other

Trigonometry: Part 2Ratios in similar trianglesMenu On page 1 of your note packet there is a pair of similar triangles. Use a ruler to measure the sides.

Trigonometry: Part 2Ratios in similar trianglesMenu On page 1 of your note packet there is a pair of similar triangles. Use a ruler to measure the sides. Use centimeters

Trigonometry: Part 2Ratios in similar trianglesMenu On page 1 of your note packet there is a pair of similar triangles. Use a ruler to measure the sides. You should get 3.7cm for the hypotenuse of the smaller triangle 3.75

Trigonometry: Part 2Ratios in similar trianglesMenu On page 1 of your note packet there is a pair of similar triangles. Use a ruler to measure the sides After you have the measures from the smaller triangle, find the measures in the larger one.

Trigonometry: Part 2Ratios in similar trianglesMenu Next, get a calculator, and fill out the tables You are going to get decimals for these answers, keep 2 decimal places.

Trigonometry: Part 2Ratios in similar trianglesMenu After you complete the table for the small triangle, measure the sides of the large triangle and complete the 2 nd table Use Centimeters

Trigonometry: Part 2Ratios in similar trianglesMenu The answers should be very close. The only reason they are different is because of imperfect measurements

Trigonometry: Part 2Ratios in similar trianglesMenu There is a simple pattern, identify it and answer questions 2-1 and 2-2 on page 2

Trigonometry: Part 3Creating Similar TrianglesMenu The pattern you should have identified in 2-1 and 2-2 is true for those triangles.

Trigonometry: Part 3Creating Similar TrianglesMenu The pattern you should have identified in 2-1 and 2-2 is true for those triangles. Is it true for any similar triangle?

Trigonometry: Part 3Creating Similar TrianglesMenu The pattern you should have identified in 2-1 and 2-2 is true for those triangles. Is it true for any similar triangle? We are going to find out by creating another, larger similar triangle.

Trigonometry: Part 3Creating Similar TrianglesMenu Step 1: on page 2, Use a ruler to draw segment AB. Make it as long as you like. Write the measurement beneath the segment Step 1: on page 2, Use a ruler to draw segment AB. Make it as long as you like. Write the measurement beneath the segment

Trigonometry: Part 3Creating Similar TrianglesMenu 15cm

Trigonometry: Part 3Creating Similar TrianglesMenu Step 2: Create a 35 0 angle at point A 15cm

Trigonometry: Part 3Creating Similar TrianglesMenu Step 2: Create a 35 0 angle at point A Line up the hole on the protractor with point A Make sure segment AB passes through 0 0.

Trigonometry: Part 3Creating Similar TrianglesMenu Step 2: Create a 35 0 angle at point A Locate 35 0, and put a mark on your paper there

Trigonometry: Part 3Creating Similar TrianglesMenu Step 2: Create a 35 0 angle at point A Draw a ray from point a through that point 35 0

Trigonometry: Part 3Creating Similar TrianglesMenu Step 3: Create a 90 0 angle at point B 35 0

Trigonometry: Part 3Creating Similar TrianglesMenu Step 3: Create a 90 0 angle at point B Line up the hole on the protractor with point B Make sure segment AB passes through

Trigonometry: Part 3Creating Similar TrianglesMenu Step 3: Create a 90 0 angle at point B Put a mark at

Trigonometry: Part 3Creating Similar TrianglesMenu Step 3: Create a 90 0 angle at point B Name the point where they touch C

Trigonometry: Part 3Creating Similar TrianglesMenu C You have now created another triangle it should be similar to the two triangles on page 1 Measure the sides, fill out the table and answer 3-1 and

If you measured PERFECTLY, your answers should be the same as those on page 1. Most likely, your measurements and therefore calculations will be very close, but NOT perfect. That’s OK.