3162009 Warm Up Determine whether the pair of

3/16/2009: Warm - Up

Determine whether the pair of figures is similar. Justify your answer. Q

Determine whether the pair of figures is similar. Justify your answer. T

An architect prepared a 12 -inch model of a skyscraper to look like a real 1100 -foot building. What is the scale factor of the model compared to the real building?

A space shuttle is about 122 feet in length. The Science Club plans to make a model of the space shuttle with a length of 24 inches. What is the scale factor of the model compared to the real space shuttle?

The two polygons are similar. Write a similarity statement. Then find x, y, and UV.

The two polygons are similar. Find the scale factor of polygon ABCDE to polygon RSTUV.

Rectangle WXYZ is similar to rectangle PQRS with a scale factor of 1. 5. If the length and width of rectangle PQRS are 10 meters and 4 meters, respectively, what are the length and width of rectangle WXYZ?

Plan Create a proportion relating the measurements to the scale to find the distance in miles. Then use the formula to find the time. Solve Cross products Divide each side by 0. 25. The distance across the city is 30 miles.

Questions? • Are there any questions about 6. 1 or 6. 2? • You will have a quiz tomorrow on this material plus 6. 3

6. 3: Similar Triangles • What we will learn today: • Identify similar triangles • Use similar triangles to solve problems

Triangle Similarity • AA Similarity: • Two angles of one triangle are congruent to two angles of another triangle.

Triangle Similarity • SSS Similarity: • The measures of the corresponding sides of two triangles are proportional

Triangle Similarity • SAS Similarity: • The measures of two sides of one triangle are proportional to the measures of two corresponding sides of another triangle, and the included angles are congruent

In the figure, and Determine which triangles in the figure are similar. Answer: Therefore, by the AA Similarity Theorem,

In the figure, OW = 7, BW = 9, WT = 17. 5, and WI = 22. 5. Determine which triangles in the figure are similar. I Answer:

ALGEBRA Given QT 2 x 10, UT 10, find RQ and QT. Answer:

ALGEBRA Given and CE x + 2, find AC and CE. Answer:

Josh wanted to measure the height of the Sears Tower in Chicago. He used a 2 -foot light pole and measured its shadow at 1 P. M. The length of the shadow was 2 feet. Then he measured the length of the Sears Tower’s shadow and it was 242 feet at that time. What is the height of the Sears Tower? Answer: The Sears Tower is 1452 feet tall.

On her trip along the East coast, Jennie stops to look at the tallest lighthouse in the U. S. located at Cape Hatteras, North Carolina. At that particular time of day, Jennie measures her shadow to be 1 feet 6 inches in length and the length of the shadow of the lighthouse to be 53 feet 6 inches. Jennie knows that her height is 5 feet 6 inches. What is the height of the Cape Hatteras lighthouse to the nearest foot? Answer: 196 ft

Classwork

3/17/2009: Warm - Up

Quiz Review

6. 4: Parallel Lines and Proportional Parts • What we will learn today: • Use proportional parts of triangles • Divide a segment into parts

Triangle Proportionality Theorem • In any triangle, a line parallel to one side of a triangle separates the other two sides proportionally. • The converse is also true

In and Find SU. S

In and B Answer: 15. 75 Find BY.

In whether and Explain. Determine

In Determine whether and AZ = 32. Explain. X Answer: No; the segments are not in proportion since

Midsegment • If X and Y are midpoints of RT and ST, then SY is a midsegment. • The midsegment is parallel to the third side and is half its length.

• When three or more parallel lines are cut by two transversals, they separate the transversals into proportional parts. • If the ratio of the parts is 1, then the parallel lines are cut into equal parts.

In the figure, Larch, Maple, and Nuthatch Streets are all parallel. The figure shows the distances in city blocks that the streets are apart. Find x.

In the figure, Davis, Broad, and Main Streets are all parallel. The figure shows the distances in city blocks that the streets are apart. Find x. Answer: 5

Find x and y.

Find a and b. Answer: a = 11; b = 1. 5

6. 5: Parts of Similar Triangles • What we will learn: • Recognize and use proportional relationships of corresponding perimeters of similar triangles • Recognize and use proportional relationships of corresponding angle bisectors, altitudes, and medians of similar triangles

Proportional Perimeters Theorem • If two triangles are similar, then the perimeters are proportional to corresponding sides

If and find the perimeter of C

If RX = 20, find the perimeter of and R Answer:

Special Segments • If two triangles are similar, then the following are all true: • Corresponding altitudes are proportional to corresponding sides • Corresponding angle bisectors are proportional to corresponding sides • Corresponding medians are proportional to corresponding sides

In the figure, and is an altitude of Find x if K

In the figure, and is an altitude of Find x if N

The drawing below illustrates two poles supported by wires. , , and Find the height of the pole.

The drawing below illustrates the legs, of a table. The top of the legs are fastened so that AC measures 12 inches while the bottom of the legs open such that GE measures 36 inches. If BD measures 7 inches, what is the height h of the table?

Classwork

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