Name: Date: 4.3.1: Introduction To Similar Polygons (1) Find the intersection point of these two lines: y = 83 x − 2 and y = (2) Find the intersection point of these two lines: y − THIS EXAMPLE DONE ON HAIKU VIDEO −3 8 x + 2 1 = 3x and y + 4 = 2 −1 2 ( x − 1) (3) Mathematicians use the term similar figures to describe figures, which have the same shape, but proportional sizes. From this very basic definition, answer the following questions. (a) Do you think all squares are similar? (c) Do you think all right triangles are similar? (b) Do you think all rectangles are similar? (d) Do you think all equilateral triangles are similar? (4) Tell whether the polygons are always, sometimes, or never similar. (Just write, A, S, or N!) (a) 2 equilateral triangles (h) Two isosceles trapezoids (b) Two right triangles (i) Two regular hexagons (c) Two isosceles triangles (j) Two regular polygons (d) Two scalene triangles (k) A right triangle and an acute triangle (e) Two squares (l) An isosceles triangle and a scalene triangle (f) Two rectangles (g) Two rhombuses The quadrilaterals shown below are similar. SOLUTION POSTED ON HAIKU (5) What is the scale factor of quad. TUNE to quad. T’U’N’E’? E (6) Find m∠T’. (7) Find the length UN. 5k (8) Find the length T’U’. E' (9) Find the length TE. (10) Find the ratio of the perimeters. 21 (11) Two similar polygons are shown at 15 right. Find the values of x, y, and z. 27 T 16 U 135° 28 N T' U' 15 35 N' x y 20 18 z ANSWERS: 16 (1) ( ,0) 3 8 41 (2) ( − , − ) 7 14 (3) a. Yes b. No. Their angles are all the same, but their sides don’t HAVE to be proportional. c. No. Their angles aren’t all the same. d. Yes. Their angles are all the same and, since there’s only one side length in each triangle, we can show that the sides are all proportional. (4) a. A b. S c. S d. S e. A f. S g. S h. S i. A j. S k. N l. N 5 (5) 4 (6) 135° (7) 12 (8) 20 (9) 4k 5 (10) 4