Solving Real World Problems using Properties of Congruent and Similar Polygons

In this mathematical problem, an observer standing near a shoreline sees a ship and is asked to determine the distance from the shoreline to the ship. The problem

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Slide2ma.912.g.2.3: use properties of congruent and similar polygons to solve mathematicalor real-world problems. An observer standing near a shoreline sees a ship. Given the measurements shown in the figure, how far is the ship from the shoreline, to the nearest  meter ? A. 139 meters B. 150 meters C. 174 meters D. 189 meters

Slide3ma.912.g.2.3: use properties of congruent and similar polygons to solve mathematicalor real-world problems. Anderson Pipe Company wants to know the distance from point  A  to point  B  across the river near their office building. They made the measurements shown in the diagram below. What is the distance across the river,  in meters ? A.  10 meters B.  20 meters C.  40 meters D.  60 meters

Slide4ma.912.g.2.3: use properties of congruent and similar polygons to solve mathematicalor real-world problems. Anita wanted to know the distance across a ravine. She constructed Δ OPQ  similar to Δ OXY . She measured  OP,  OX, and  XY  and recorded the distances as shown.  What is the length of  PQ ? A.  175 m B.  200 m C.  262 m D.  434 m

Slide5ma.912.g.2.3: use properties of congruent and similar polygons to solve mathematicalor real-world problems.

Slide6ma.912.g.2.3: use properties of congruent and similar polygons to solve mathematicalor real-world problems.

Slide7ma.912.g.2.3: use properties of congruent and similar polygons to solve mathematicalor real-world problems. Which of the following must be true in order to make a true statement?

Slide8ma.912.g.2.3: use properties of congruent and similar polygons to solve mathematicalor real-world problems. The side length of square ABCD  is 1 unit. Its diagonal, AC , is a side of square  ACEF . Square  ACEF  is then enlarged by a scale factor of 2. What is the area of the enlargement, in square units ? A. 1 square unit B. 2 square units C. 4 square units D. 8 square units

Slide9ma.912.g.2.: use properties of congruent and similar polygons to solve mathematical orreal-world problems. Which of the triangles is an equilateral triangle? A C B D

Slide10ma.912.g.2.3: use properties of congruent and similar polygons to solve mathematicalor real-world problems. Greg wanted to know the distance across a pond. He constructed Δ DEF similar to Δ DGH . He measured DE, DG, and GH and recorded the distances as shown. What is the length of EF? A.  127 m B.  210 m C.  303 m D.  348 m

Slide11ma.912.g.2.3: use properties of congruent and similar polygons to solve mathematicalor real-world problems. Given Δ ABC  and  DE  is parallel to  AC , which of the following is true?

Slide12ma.912.g.2.3: use properties of congruent and similar polygons to solve mathematicalor real-world problems. Which correctly explains why triangle ABC  is similar to triangle  EDC ?

Slide13ma.912.g.2.3: use properties of congruent and similar polygons to solve mathematicalor real-world problems. Given Δ ABC  and    is parallel to    , what is the length of    ?