1 / 13

9.2 Similar Polygons

9.2 Similar Polygons. Vocabulary. Similar Polygons . What You'll Learn. You will learn to identify similar polygons . . 1) polygons 2) sides 3) similar polygons 4) scale drawing. D. Δ ABC is similar to Δ DEF. A. C. B. F. E. Similar Polygons .

taro
Download Presentation

9.2 Similar Polygons

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 9.2 Similar Polygons

  2. Vocabulary Similar Polygons What You'll Learn You will learn to identify similar polygons. 1) polygons 2) sides 3) similar polygons 4) scale drawing

  3. D ΔABC is similar toΔDEF A C B F E Similar Polygons A polygon is a ______ figure in a plane formed by segments called sides. closed It is a general term used to describe a geometric figure with at least three sides. Polygons that are the same shape but not necessarily the same size are called ______________. similar polygons The symbol ~ is used to show that two figures are similar. ΔABC ~ ΔDEF

  4. and D C G H E F A B Similar Polygons proportional Polygon ABCD~ polygon EFGH

  5. 6 4 5 7 5 7 4 6 = Similar Polygons Determine if the polygons are similar. Justify your answer. 6 4 5 7 1) Are corresponding angles are _________. congruent 2) Are corresponding sides ___________. proportional 0.66 = 0.71 The polygons are NOT similar!

  6. R 5 Write the proportion thatcan be solved for y. 4 J S T 6 x = 7 Write the proportion thatcan be solved for x. = K L y + 2 Similar Polygons Find the values of x and y if ΔRST ~ ΔJKL 6 4 y + 2 7 4(y + 2) = 42 4y + 8 = 42 5 4 4y = 34 x 7 4x = 35

  7. 1.25 in. 1 in. .5 in. = = Utility Room Kitchen Dining Room length width .75 in. Living Room 1.25 in. Garage Scale: 1 in. = 16 ft. Similar Polygons Scale drawings are often used to represent something that is too large or too small to be drawn at actual size. Contractors use scale drawings to represent the floorplan of a house. Use proportions to find the actual dimensions of the kitchen. 1.25 in. .75 in. 1 in 1 in L ft. w ft. 16 ft 16 ft (16)(1.25) = w (16)(.75) = L 20 = w 12 = L width is 20 ft. length is 12 ft.

  8. Vocabulary Perimeters and Similarity What You'll Learn You will learn to identify and use proportional relationships of similar triangles. 1)Scale Factor

  9. perimeter of small Δ 6 + 8 + 10 24 2 = = = perimeter of large Δ 9 + 12 + 15 36 3 Perimeters and Similarity These right triangles are similar! Therefore, the measures of their corresponding sides are ___________. proportional Pythagorean Use the ____________ theoremto calculate the length of the hypotenuse. 10 6 15 9 8 12 10 2 8 6 We know that = = = 15 3 12 9 Is there a relationship between the measures of the perimeters of the two triangles?

  10. D A C B F E perimeter of ΔABC CA AB BC = = = FD perimeter of ΔDEF DE EF Perimeters and Similarity the measures of the corresponding perimeters are proportional to the measures of the corresponding sides. If ΔABC ~ ΔDEF, then

  11. M 4.5 R z 3 T P x 6 Y N S perimeter of ΔMNP NP PM MN MN MN = = = ST TR RS RS RS perimeter of ΔRST 6 4.5 3 3 13.5 3 = = = y z 2 2 x 9 y = 4 x = 2 z = 3 Perimeters and Similarity The perimeter of ΔRST is 9 units, and ΔRST ~ ΔMNP. Find the value of each variable. Theorem 9-10 The perimeter of ΔMNP is 3 + 6 + 4.5 3y = 12 3z = 9 27 = 13.5x Cross Products

  12. A 5 3 C B 7 CA BC AB = = FD EF DE D or 7 5 3 = = 10 6 6 14 10 1 2 1 2 2 1 E F 14 Perimeters and Similarity The ratio found by comparing the measures of corresponding sides of similar triangles is called the constant of proportionality or the ___________. scale factor If ΔABC ~ ΔDEF, then The scale factor of ΔABC to ΔDEF is Each ratio is equivalent to The scale factor of ΔDEF to ΔABC is

  13. End of section 9.2

More Related