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# (7.3) Patterns, relationships, and algebraic thinking.

7.3B Problem Solving with Similar Figures. (7.3) Patterns, relationships, and algebraic thinking. The student solves problems involving proportional relationships.

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## (7.3) Patterns, relationships, and algebraic thinking.

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1. 7.3B Problem Solving with Similar Figures (7.3) Patterns, relationships, and algebraic thinking. The student solves problems involving proportional relationships. The student is expected to: (B) estimate and find solutions to application problems involving proportional relationships such as similarity, scaling, unit costs, and related measurements.

2. 7.3B INSTRUCTIONAL ACTIVITY #1 Over the past two days you’ve used proportions in problem solving involving percents. Another type of real-life problem that can be solved using a proportion is a problem involving similar figures. Similar figures are geometric figures that have the same shape but not necessarily the same size. In similar figures the ratios of the lengths of corresponding sides are proportional. Corresponding sides are sides that are in the same relative position in the two figures.

3. In the example below, rectangle EFGH is similar to rectangle JKLM. What is the length of side FG in rectangle EFGH? F 18 E J K 6 • HG corresponds to ML • EH corresponds to MJ • EF corresponds to JK • FG corresponds to KL x 8 L M H G • Corresponding sides of similar figures are sides that are in the same relative position. • If two figures are similar, then the ratios of Corresponding sides form a proportion. largeEFFG small JK KL =

4. In the example below, rectangle EFGH is similar to rectangle JKLM. What is the length of side FG in rectangle EFGH? F 18 E J K 6 x 18 FG EF Use cross products to write an equation. x 8 = JK KL 6 8 L M H G 6 • x = 18 • 8 • Substitute the lengths of the sides in the proportion. 6x = 144 Divide both sides of the equation by 6. 6 6 • To find the value of x, solve the proportion. x = 24 The length of side FG is 24 units.

5. Two similar polygons can also have corresponding angles that are congruent and corresponding sides that are proportional. In the example below, are ΔABC and ΔEFD similar? E 2 B C 17° 29° 134° 9 3 6 4.5 17° 134° 29° F D A 4 • Corresponding angles of similar figures are congruent. LA is congruent to LE LB is congruent to LF LC is congruent to LD

6. Two similar polygons can also have corresponding angles that are congruent and corresponding sides that are proportional. In the example below, are ΔABC and ΔEFD similar? E 2 B C 17° 29° 134° 9 3 6 4.5 17° 134° 29° A F D 4 • Corresponding sides of similar figures are in the same relative position and are proportional. 1 6 2 2 1 4 2 4.5 1 9 2 AB corresponds to EF ΔABC and ΔDEF have corresponding angles that are congruent and corresponding sides that are proportional. therefore ΔABC and ΔEFD are similar. = = = BC corresponds to DF AC corresponds to DE

7. For the rest of the class period work on 7.3B Student Activity #1 in your binders. Be prepared for a mini-assessment tomorrow!

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