Similar Figures and Indirect Measurement Review: Solve each Proportion, Round to the Nearest Tenth Where Necessary. You may use your calculators. 2 3 f = 21 f = 14 3 8 50 = p p = 133.3 z = 6.7 9 4 15 = z g = 3.6 16 3 19 = g Similar Figures Figures that are SIMILAR have the SAME SHAPE, but NOT necessarily the same SIZE. Similar Figures have the Same Angles and Sides they are called Corresponding Angles and Corresponding Sides. Corresponding = The Same These Figures Are Similar The symbol ~ means “is similar to”. X To the right, 53° A 9 53° ΔABC ~ ΔXYZ. 15 90° Y 10 90° 37° 37° 12 C Z 6 8 B Properties of Similar Figures The Corresponding angles have equal measures. The lengths of the corresponding sides are in proportion. Example Problems Parallelogram ABCD ~ parallelogram EFGH. Find the value of X. Hint: Write a proportion for corresponding sides. 24 E A 16 F B 18 X D C H Corresponding Sides go Together. Write the CROSS PRODUCT. G X 18 (X)(24) = (18)(16), X = 12 16 = 24 Try This… Parallelogram KLMN is similar to parallelogram ABCD in the previous example. Find the value of Y. Remember, X = 12 on Parallelogram ABCD. A 16 B 21 L Y X D K C N M Indirect Measurements Similar Figures can be used to measure things that are difficult to measure otherwise. use PROPORTIONS! Indirect Measurements A tree casts a shadow of 10 feet long. A 5 foot woman casts a shadow of 4 feet. The triangle shown for the woman and her shadow is similar to the triangle shown for the tree and its shadow. How tall is the tree? The tree is 12.5 feet tall. D REMEMBER to CHECK RATIOS!!! THIS compared to THAT. THIS AND THAT have to be in the same ORDER every TIME!!! Try This One and Draw It Yourself A building is 70 feet high and casts a 150 foot shadow. A nearby flagpole casts a 60 foot shadow. Draw a picture/diagram of the building, the building’s shadow, the flagpole, and it’s shadow. Use the triangles created to find the height of the flagpole. Scale Drawings Scale Drawings are enlarged or reduced drawings that are SIMILAR to an ACTUAL object or place. The RATIO of a distance in the drawing (or representation) to the corresponding actual distance is the SCALE of the drawing. Guess Where This Is… This is the ratio for this Scale Representation! Try This One… The scale of the map is 50 m : 200 ft. About how far from Robinson Road is SE 6th Ave, if the map distance is 150m? Write a proportion. Write Cross Products. Simplify.