1 / 14

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

mabraham
Download Presentation

Unit 23

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related