CONGRUENT AND SIMILAR FIGURES 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 The angles that lie opposite equal sides are corresponding angles

CONGRUENT FIGURES A B C D 5" 4.75" 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

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

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

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' A B C D A' B' C' D' 15.75" 16" 3.25" 3" 6"

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

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

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

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

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 A B C D E F 10" 13.5" 12.5" 11.5" 9" 11" A B C D E F 8"

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. A B E C D

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

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