Warm up… Reflect on the first six weeks. What will you as an individual do differently this six weeks to achieve the grade you want in this class? Whether is be attend tutoring, study better, do test corrections, work harder on ACC math, complete all assignment and/or complete the six weeks project. This needs to be in paragraph form.

8.1 Proportions

SWBAT… Write ratios and solve proportions

What do you remember?

In case you forgot… A ratio is a comparison of two quantities. The ration of a to b can be expressed as where b is NOT zero

Example 1 Last year, of the 270 high school students at CVC, 190 of them participated in some kind of sport. Find the athlete to student ratio to the nearest tenth.

Putting it to work in Geometry In a triangle, the ratio of the measure of the three sides is 5:12:13, and the perimeter is 90 cm. Find the length of the shortest side.

Properties of Proportions An equations stating that two ratios are equal is called a proportion Equivalent fractions are set equal to each other to form a proportion. Every proportions has two cross products. Extremes Means

More on properties of proportions For any numbers a and c, and any nonzero number b and d, if and only if ad = bc

Example 3 Solve each proportion

Example 4 A boxcar on a train has a length of 40 feet and a width of 9 feet. A scale model made with a length of 16 inches, find the width of the model.

You try… Page # 2 – 24 We’ll go over it in 7 minutes

8.2 Similar Polygons

SWBAT… To identify similar polygons To apply similar polygons

Similarity When figures have the same shape but different sizes we call them similar figures. ~ is our symbol for similarity

Ex. 1: Writing Similarity Statements Given: JKLMN ~ STUVW you can write  J   S,  K   T,  L   U,  M   V AND  N   W. You can write the proportionality statement as follows: KL TU = JK = ST MN VW = LM = UV NJ WS

Ex. 2: Comparing Similar Polygons Decide whether the figures are similar. If they are similar, write a similarity statement.

Ex. 3: Comparing Photographic Enlargements POSTER DESIGN. You have been asked to create a poster to advertise a field trip to see the Liberty Bell. You have a 3.5 inch by 5 inch photo that you want to enlarge. You want the enlargement to be 16 inches wide. How long will it be?

Solution: To find the length of the enlargement, you can compare the enlargement to the original measurements of the photo. 16 in. 3.5 in. = x in. 5 in.  The length of the enlargement will be about 23 inches

Using similar polygons in real life If two polygons are similar, then the ratio of lengths of two corresponding sides is called the scale factor. In Example 2 on the previous page, the common ratio of is the scale factor of WXYZ to PQRS. 3 2

Ex. 4: Using similar polygons The rectangular patio around a pool is similar to the pool as shown. Calculate the scale factor of the patio to the pool, and find the ratio of their perimeters. 16 ft24 ft 32 ft 48 ft

Because the rectangles are similar, the scale factor of the patio to the pool is 48 ft: 32 ft., which is 3:2 in simplified form. The perimeter of the patio is 2(24) + 2(48) = 144 feet and the perimeter of the pool is 2(16) + 2(32) = 96 feet The ratio of the perimeters is 16 ft24 ft 32 ft 48 ft , or

NOTE: Notice in Example 4 that the ratio of perimeters is the same as the scale factor of the rectangles. This observation is generalized in the following theorem.

Theorem If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding parts. If KLMN ~ PQRS, then KL + LM + MN + NK PQ + QR + RS + SP = KL PQ LM QR MN RS NK SP = = =

Ex. 5: Using Similar Polygons Quadrilateral JKLM is similar to PQRS. Find the value of z. Set up a proportion that contains PQ KL QR JK PQ = Z = Z = 4 Write the proportion. Substitute Cross multiply and divide by 15.

You try… Page 425 – 426 #’s 2 – 18 even Take 7 minutes to complete those and we’ll go over them

Class work… Page 419 #’s 26 – 42 evens Page 426 – 427 #’s

Closing… Your homework is pages 428 and 429 #’s 53 – 66 and the checkpoint quiz on the bottom of page 429. On your index card answer the follow. 3.5 cm Find the value of x. Given that 7 cm P S R T Q 5.2 cm x