8.4 Similar Triangles UNIT IIA DAY 4

Do Now What is the altitude of a triangle? a segment from a vertex perpendicular to the opposite side of a triangle.

Ex. 4A: Using Similar Triangles In another camera, f = 10 cm and n = 6 cm. Estimate the altitude required to take a photo the covers a ground distance of 100 m. about 167 meters f h n g =

More About Similarity If two polygons are similar, then the ratio of any two corresponding lengths (such as altitudes, medians, angle bisector segments, and diagonals) is equal to the scale factor of the similar polygons. Recall: We already knew this was true for ____________ perimeters

Ex. 5: Using Scale Factors Find the length of the altitude QS. Find the scale factor of ΔNQP to ΔTQR. NP/TR (12+12)/(8+8) = 24/16 = 3/2 Now, because the ratio of the lengths of the altitudes is equal to the scale factor, you can write the following equation. QM/QS = 3/2 We know QM = 6, so substitute and solve for QS to show that QS = 4.

Ex. 1 A In the diagram, ΔLMN ~ ΔPQN. Write a statement of proportionality. Find m M and m P. Find MN and QM. PQ/LM = QN/MN = NP/NL 36º, 38º (corresponding angles congruent) 22 (solve proportion), 42 (segment addition)

Ex. 2A Explain why ΔWVX ~ ΔWZY. Both triangles share W (reflexive) and both have a right angle (all right angles are congruent). By AA, the triangles are similar.

Ex. 5A Find the length of EH. First of all, is ∆ACD ~ ∆AEB? Both share A (reflexive) and C marked = E, so similar by AA. 5/(5 + 7.5) = 6/x x = 15

Ex. 6 The company logo shown consists of two equilateral triangles. If the scale factor between the two triangles is 5:2, how long is a side of the smaller equilateral triangle? Suppose in an enlarged version of the logo, the smaller triangle has a side length of 4.5 cm. How long is a side of the larger triangle? 1.8 cm 11.25 cm