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What properties allow transformation to be used as a problem solving tool

Look at the figure below: triangle abc is a right triangle with angle abc equal to 90 degrees. the length of ac is 5 units and the length of ab is 4 units. d is a point above c. triangle adc is a right triangle with angle dac equal to 90 degrees and dc parallel to ab. what is the length, in units, of segment cd?

Identify this conic section. x2 - y2 = 16 o line circle ellipse parabola hyperbola