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1 In the Overview you met Bud and Travis the dirt bike enthusiasts To determine if they can cross a ravine Bud measures distances and angles using a cactus branch to create two congruent triangles For the measurements to work Bud makes sure that the angle of his line of sight with the top of the pole is the same when he sights parallel to the ravine as when he was sighting across the ravine far edge ravine BU B U B2B pole ZU ZU near edge Bud triangle BU represents Bud when his line of sight travels to the top of the pole labeled L and to a point on the opposite edge of the ravine labeled D B U represents Bud s position after he walks from the pole in the direction parallel with the edge of the ravine B U and BU are both Bud s height In both triangles LP represents the pole Based on the method Bud used justify the reason you know the parts in each pair are congruent A a The two triangles above represent the walk that Bud took The first D feet R b Based on the logical arguments you developed in part a what two triangles can you prove congruent How do you know they are congruent ravine B A by c The image below shows Bud s measurements How do these two triangles help justify Bud s estimation that the ravine is less than 25 feet wide opposite edge B U

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