Unit 23 CONGRUENT AND SIMILAR FIGURES 1 CONGRUENT
- Slides: 14
Unit 23 CONGRUENT AND SIMILAR FIGURES 1
CONGRUENT FIGURES Congruent figures have exactly the same size and shape. The symbol means congruent p Corresponding parts of congruent triangles are equal p n n The sides that lie opposite equal angles are corresponding sides The angles that lie opposite equal sides are corresponding angles 2
CONGRUENT FIGURES B 5" 4. 75" A • BCA and CAD are corresponding angles because they are both opposite 5" long sides C 4. 75" 5" • BAC and ACD are corresponding angles because they are both opposite 4. 75" long sides D 3
SIMILAR FIGURES Similar figures mean figures that are alike in shape but different in size p Similar polygons have the same number of sides, equal corresponding angles, and proportional corresponding sides p The symbol ~ means similar p 4
SIMILAR FIGURE EXAMPLE p Given that the two polygons shown below are similar and A = A', B = B', C = C', and D = D’, then 3" A D 15. 75" C 3. 25" B 16" The corresponding sides are proportional as follows: C' D' 6" A' B' 5
SIMILAR FIGURE EXAMPLE (Cont) p Given that the two polygons shown below are similar and A = A', B = B', C = C', and D = D’, 3" A D 15. 75" C 3. 25" Determine the lengths of sides (a) A'B', (b) B'C', and (c) C'D' B 16" C' D' 6" A' B' 6
SIMILAR TRIANGLES If two angles of a triangle are equal to two angles of another triangle, the triangles are similar p If the corresponding sides of two triangles are proportional, the triangles are similar p 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 p 7
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 p 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 p 8
SIMILAR TRIANGLES EXAMPLE p Determine AD and DC in the right triangle shown below: – BD AC so ABC ~ ABD ~ BDC A 25 20 mm B D 15 mm m m C DC = AC – AD = 25 mm – 16 mm = 9 mm Ans 9
PRACTICE PROBLEMS 1. Identify the pairs of corresponding angles in the figure below: B 4" A C 5" 3" 5" E 4" 3" D 10
PRACTICE PROBLEMS (Cont) 2. The two polygons below are similar. A = A , B = B , C = C , D = D , E = E , F = F. Find each of the following: a) b) c) d) Side BC CD DE AF A 8" A 10" B C F D E 11" B 13. 5" F 9" C 12. 5" E 11. 5" D 11
PRACTICE PROBLEMS (Cont) 3. 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 12
PRACTICE PROBLEMS (Cont) 4. Determine length F in the figure below given that AB = 32 m and AC = 10 m. 50 m F A C B 13
PROBLEM ANSWER KEY 1. 2. 3. 4. 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 14