Using Similar Triangles and Rectangles Investigation 5 Similar triangles can be used to estimate heights and distances that are too difficult to measure directly. How do we know the triangles are similar? 1) The tower and the stick form a right angle with the ground. 2) The angle at the base of each triangle is the angle of the sun. From two nearby points at a common time, the sun appears at the same angle. 3) The 3rd angle must be the same in each triangle because all 3 angles must = 180°. 3 3 stick 1 2 1 2 shadow shadow

5.1 Using Shadows to Find Heights TWO ways to SOLVE: What is the height of the clock tower? Find scale factor 6 = 2 3 Multiply by scale factor 3 x 2 = 6 cm x = 10 cm 5 x 2 = 10 cm OR x 5 cm Set up adjacent side ratios x = 5 6 3 Find equivalent fractions 10 ÷ 2 = 5 x = 10 cm 6 ÷ 2 = 3 6 cm 3 cm

5.2 Using Mirrors to Find Heights What is the height of the street light? TWO ways to SOLVE: Find scale factor 4.5 = 3 1.5 Multiply by scale factor 1.5 x 3 = 4.5 m x = 9 m 3 x 3 = 9 m Set up adjacent side ratios x = 3 4.5 1.5 Find equivalent fractions 9 ÷ 3 = 3 x = 9 m 4.5 ÷ 3 = 1.5 x 3 m 4.5 m 1.5 m Light reflects off a mirror at the same angle so these angles are congruent.

5.3 On the Ground…but Still Out of Reach Now solve for the missing length like before! Can you see 2 similar triangles? A A A 2 B C C B 1 E D D E <A has the same measure in both triangles because they share vertices. <B & <D and <C & <E have the same measure because they are corresponding angles created by a transversal crossing two parallel lines.