University:
Felician University
Course:
MATH-160 | College Algebra
Academic year:

2019
Views:

111

Pages:

2
Author:

SpaceCadet101

Practice Similar Polygons List the pairs of congruent angles and the extended proportion that relates the corresponding sides for the similar polygons. 1. ABCD ~ WXYZ ∠A ≅ ∠W, ∠B ≅ ∠X, ∠C ≅ ∠Y, ∠D ≅ ∠Z; AB/WX = BC/XY = CD/YZ = DA/ZW 2. ΔMNO ~ ΔRST ∠M ≅ ∠R, ∠N ≅ ∠S, ∠O ≅ ∠T; MN/RS = NO/ST = OM/TR 3. NPOM ~ TORS ∠N ≅ ∠T, ∠P ≅ ∠Q, ∠O ≅ ∠R, ∠M ≅ ∠S; NP/TQ = PO/QR = QM/RS = MN/ST Determine whether the polygons are similar. If so, write a similarity statement and give the scale factor. If not, explain. 4. MNOP ~ URST or MNOP ~ STUR; 2:3 5. not similar; corresponding angles not congruent 6. not similar; corresponding sides not proportional 7. an equilateral triangle with side length 6 and an equilateral triangle with side length 15 yes 8. a square with side length 4 and a rectangle with width 8 and length 8.5 no 9. a triangle with side lengths 3 cm, 4 cm, and 5 cm, and a triangle with side lengths 18 cm, 19 cm, and 20 cm no 10. a rhombus with side lengths 8 and consecutive angles 50° and 130°, and a rhombus with side lengths 13 and consecutive angles 50° and 130° yes Practice (continued) Similar Polygons 11. An architect is making a scale drawing of a building. She uses the scale 1 in. = 15 ft. a. If the building is 48 ft tall, how tall should the scale drawing be? 3.2 in. b. If the building is 90 ft wide, how wide should the scale drawing be? 6 in. 12. A scale drawing of a building was made using the scale 15 cm = 120 ft. If the scale drawing is 45 cm tall, how tall is the actual building? 360 ft Determine whether each statement is always, sometimes, or never true. 13. Two squares are similar. always 14. Two hexagons are similar. sometimes 15. Two similar triangles are congruent. sometimes 16. A rhombus and a pentagon are similar. never Algebra Find the value of y. Give the scale factor of the polygons. 17. ABCD ~ TSVU 7.5:2:3 3y - 3.5 3y - 3.5 3y + 6 3y + 6 18. The scale factor of RSTU to VWXY is 1:4. What is the scale factor of VWXY to RSTU? 4:1 In the diagram below, ΔPRQ ~ ΔDEF. Find each of the following. 19. the scale factor of ΔPRQ to ΔDEF 5:6 20. m∠D 56° 21. m∠R 35° 22. m∠P 56° 23. DE 48 24. FE 43.2 25. Writing Explain why all isosceles right triangles are similar, but not all scalene right triangles are similar. Answers may vary. Sample: All isosceles right triangles have angle measures 45-45-90, the legs of the triangle will always be congruent, and the hypotenuses are always about 1.4 times the length of the leg. Scalene right triangles can have any pair of angle measures that adds up to 90 for the non-right angles, so they are not all similar.