7 3 Proving Triangles Similar Think back How

7. 3 Proving Triangles Similar

Think back… � How can we determine whether triangles and polygons are similar? ◦ Polygons are similar if corresponding sides are proportional and corresponding angles are congruent. ◦ Today, we will learn how to determine if they are similar using an easier way.

Angle-Angle (AA)Similarity Postulate � If 2 angles of one triangle are congruent to 2 angles of a another triangles, then the 2 triangles are similar. D A ABC DEF B C E This is called a “similarity statement. ” Notice that the letters are in order with how the correspond in the triangles. F

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More ways to determine if two triangles are similar… � Side-Side (SSS): If the lengths of corresponding sides are proportional, the triangles are similar. � Side-Angle-Side (SAS): If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides that include these angle are proportional, the triangles are similar.

Ex. 2 a � Are the triangles similar? If so, write a similarity statement for the triangles.

Ex. 2 b � Are the triangles similar? If so, write a similarity statement for the triangles. How could we make this easier?

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Ex. 3: Proving Triangles Similar

Application of Similar Triangles – Similar Triangles Allow us to measure things “indirectly. ” � Why would we measure distance indirectly? ◦ We may not be able to “reach” something or measure it directly. � To find distance indirectly, you can use: �Mirror method �Shadow method �Surveying method

Shadow Method ∆ Greek mathematician Thales (640– 546 B. C. ) calculated the height of the Great Pyramid in Egypt by placing a rod at the tip of the pyramid’s shadow and using similar triangles. Approximately how tall is the pyramid? x ft 780 ft 6 ft 10 ft

Mirror Method ∆ You are visiting the Unisphere at Flushing Meadow Park in New York. To estimate the height of the stainless steel model of Earth, you place a mirror on the ground and stand where you can see the top of the model in the mirror. Use the diagram shown to estimate the height of the model.

Surveying method To measure the width of a river, you use a surveying technique, as shown in the diagram. Use the given lengths (measured in feet) to find RQ.