Vocabulary 8.1 ratio proportion cross products similar similar polygons similarity ratio scale factor

REVIEW: A ratio compares two numbers by division. The ratio of two numbers a and b can be written as a to b, a:b, or , where b ≠ 0. For example, the ratios 1 to 2, 1:2, and all represent the same comparison. A proportion is an equation stating that two ratios are equal.

Examples 1A/B: Using Properties of Proportions 1A. Solve the proportions for x. 1B. Given that 18c = 24d, find the ratio of d to c in simplest form. Next, find the ration of c to d.

Figures that are similar (~) have the same shape but not necessarily the same size.

SIMILAR FIGURES: AND RATIOS OF CORRESPONDING SIDES ARE PROPORTIONAL CORRESPONDING ANGLES ARE CONGRUENT IFF: Similar  ROCSAP AND CAAC

A Similarity Ratio is the ratio of the lengths of the corresponding sides of two similar polygons. The similarity ratio of ∆ABC to ∆DEF is , or . The similarity ratio of ∆DEF to ∆ABC is , or 2.

A Scale Factor (k) is the inverse of the similarity ratio A Scale Factor (k) is the inverse of the similarity ratio. Getting bigger k>1, smaller k<1 The scale factor of ∆ABC to ∆DEF is 2 The scale factor of ∆DEF to ∆ABC is The Similarity Ratio and the Scale Factor are the inverse of each other…

Examples 2A/B: Using Properties of Proportions A) ∆KLT ~ ∆XMJ. KT = 6, XM = 8, LT = 5, XJ = 12. Find KL & MJ. KL = 4, MJ = 10 NY = 16 , LZ = 8

Ratios of ANY corresponding lengths are equal (sides, altitudes, medians, perimeters, etc.)  

Example 3: Modeling     Find P1= 150   P2= 120

 

Example 4: Similar Areas   A2 = 756 m2

Example 5: Identifying Similar Polygons Determine whether the rectangles are similar. If so, write and a similarity statement and find the similarity ratio  

Example 6: Identifying Similar Polygons Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. Not ~

Check It Out! Example 7 Determine if ∆JLM ~ ∆NPS. If so, write the similarity ratio and a similarity statement. Check ROCSAP and CAAC Be careful about the “ORDER” in similarity statement Similar, but NOT as stated… ∆MLJ ~ ∆NPS

Example 7: Identifying Similar Polygons 7. Tell whether the following statement is sometimes, always, or never true. Two equilateral triangles are similar. Two right triangles are similar Two circles are similar Two rectangles are similar Two regular hexagons are similar A S A S A