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Unit 23

Unit 23. CONGRUENT AND SIMILAR FIGURES. CONGRUENT FIGURES. Congruent figures have exactly the same size and shape . The symbol  means congruent Corresponding parts of congruent triangles are equal The sides that lie opposite equal angles are corresponding sides

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Unit 23

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  1. Unit 23 CONGRUENT AND SIMILAR FIGURES

  2. CONGRUENT FIGURES • Congruentfigures have exactly the same size and shape. The symbol  means congruent • Corresponding parts of congruent triangles are equal • The sides that lie opposite equal angles are corresponding sides • The angles that lie opposite equal sides are corresponding angles

  3. B 5" 4.75" A C 4.75" 5" D CONGRUENT FIGURES • BCA and CAD are corresponding angles because they are both opposite 5" long sides • BAC and ACD are corresponding angles because they are both opposite 4.75" long sides

  4. SIMILAR FIGURES • Similar figures mean figures that are alike in shape but different in size • Similar polygons have the same number of sides, equal corresponding angles, and proportional corresponding sides • The symbol ~ means similar

  5. 15.75" D C 3" 3.25" A B 16" C' D' 6" A' B' SIMILAR FIGURE EXAMPLE • Given that the two polygons shown below are similar and A = A', B = B', C = C', and D = D’, then The corresponding sides are proportional as follows:

  6. 15.75" D C 3" 3.25" A B 16" C' D' 6" A' B' SIMILAR FIGURE EXAMPLE (Cont) • Given that the two polygons shown below are similar and A = A', B = B', C = C', and D = D’, Determine the lengths of sides (a) A'B', (b) B'C', and (c) C'D'

  7. SIMILAR TRIANGLES • If two angles of a triangle are equal to two angles of another triangle, the triangles are similar • If the corresponding sides of two triangles are proportional, the triangles are similar • If two sides of a triangle are proportional to two sides of another triangle and if the included angles are equal, the triangles are similar

  8. SIMILAR TRIANGLES (Cont) • Within a triangle, if a line parallel to one side intersects the other two sides, the triangle formed and the given triangle are similar • If the altitude is drawn to the hypotenuse of a right triangle, the two triangles formed are similar to each other and to the given triangle

  9. A 25 mm 20 mm D B C 15 mm SIMILAR TRIANGLES EXAMPLE • Determine AD and DC in the right triangle shown below: • BD  AC so ABC ~ ABD ~ BDC DC = AC – AD = 25 mm – 16 mm = 9 mm Ans

  10. B C 5" 5" 4" 3" D A E 3" 4" PRACTICE PROBLEMS • Identify the pairs of corresponding angles in the figure below:

  11. A 10" 11" B 13.5" F B 8" 9" A C C E 12.5" 11.5" D F D E PRACTICE PROBLEMS (Cont) • The two polygons below are similar. A = A, B = B, C = C, D = D, E = E, F = F. Find each of the following: • Side BC • Side CD • Side DE • Side AF

  12. A B E C D PRACTICE PROBLEMS (Cont) • CDE ~ ABE in the figure below. Given that AE = 70 ft, BE = 87.5 ft, EC = 25 ft, ED = 20 ft, and CD = 40 ft, find AB.

  13. 50m F A C B PRACTICE PROBLEMS (Cont) • Determine length F in the figure below given that AB = 32 m and AC = 10 m.

  14. PROBLEM ANSWER KEY • ABE and CED AEB and ECD BAE and EDC • a) 10.8 inches b) 10 inches c) 9.2 inches d) 8.8 inches • 140 feet • 15.625 m

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