8.5 congruent polygons 1

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8.5 congruent polygons 1

  1. 1. Lesson 8.5 , For use with pages 427-432 Find the sum of the angle measures in the polygon. 1. octagon 2. 21 -gon
  2. 2. Lesson 8.5 , For use with pages 427-432 Find the sum of the angle measures in the polygon. 1. octagon 2. 21 -gon ANSWER 3420º ANSWER 1080º
  3. 3. Congruent Polygons Section 8.5 P. 427 - 432
  4. 4. Essential Questions <ul><li>Why is it important to be able to identify congruent triangles in everyday life? </li></ul><ul><li>Where in real life can you use the properties of isosceles and equilateral triangles? </li></ul><ul><li>How are the relationships between lines and planes used in the real world? </li></ul><ul><li>What areas in the real world are properties of parallel lines important? </li></ul>
  5. 5. <ul><li>Now that you have classified and identified various polygon, we are going look at polygons that are congruent. Congruent polygons are polygons that are the exact same size and shape , and they are constructed of congruent angles and congruent segments. </li></ul>
  6. 6. <ul><li>Corresponding Sides and Corresponding Angles are formed when two figures are congruent. </li></ul>A B C D E F Note symbol for congruent
  7. 7. Picture Frames EXAMPLE 1 Name Corresponding Parts SOLUTION Corresponding angles are congruent. Corresponding sides are congruent. = In the frame below, quadrilateral ABCD quadrilateral JKLM . Name all pairs of corresponding angles and sides. A , B , K D , M J C , L AB, JK CD, LM BC, KL AD, JM
  8. 8. GUIDED PRACTICE for Example 1 SOLUTION Corresponding angles are congruent. Corresponding sides are congruent. 1. In Example 1 , quadrilateral EFGH quadrilateral QRNP . Name all pairs of corresponding angles and sides. = E , F , R H , P Q G , N EF, QR GN, NP FG, RN HE, PQ
  9. 9. SOLUTION EXAMPLE 2 Using Congruent Polygons Corresponding angles are congruent. Add. Subtract 56 from each side. Simplify. ANSWER JKL TSR . = Find m S . 31 + m K + 25 = 180 K and S are corresponding angles, so they have the same measure. Find m K . Sum of angle measures is 180 . = 180 m K + 56 m K + 56 – 56 = 180 – 56 m K = 124 = Because m K m S, m S = 124
  10. 10. GUIDED PRACTICE for Example 2 Find the value using the triangles in Example 2 . 2. length of ST KJ ST = 10 cm ANSWER JKL TSR . = 3. m T m J = m T = 31 ANSWER JKL TSR . = 4. m R m R = 25 ANSWER JKL TSR . =
  11. 11. Special Rules for Congruent Triangles <ul><li>Side – Side – Side (SSS) If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. </li></ul>A B C D E F
  12. 12. Special Rules for Congruent Triangles <ul><li>Side – Angle – Side (SAS) If two sides and the angle between them in one triangle are congruent to two sides and the angle between them in another triangle, then the triangles are congruent. </li></ul>A B C D E F
  13. 13. Special Rules for Congruent Triangles <ul><li>Angle – Side – Angle (ASA) If two angles and the side between them in one triangle are congruent to two angles and the side between them in another triangle, then the triangles are congruent. </li></ul>A B C D E F
  14. 14. Congruent Triangles <ul><li>Go to www.aea13.org </li></ul><ul><li>Programs and Services </li></ul><ul><ul><li>School Technology </li></ul></ul><ul><ul><li>E2T2 </li></ul></ul><ul><li>On the far left, click on Teacher’s page </li></ul><ul><li>National Library of Virtual Manipulatives </li></ul><ul><ul><li>Select Geometry 6-8 </li></ul></ul><ul><ul><li>Click on the third one down called “ Congruent Triangles ” </li></ul></ul>
  15. 15. <ul><li>Concluding: </li></ul><ul><li>Two triangles are congruent if: </li></ul><ul><li>SSS </li></ul><ul><li>SAS </li></ul><ul><li>ASA </li></ul>
  16. 16. SOLUTION EXAMPLE 3 Identifying Congruent Triangles Bridges Identify congruent corresponding parts. Sides are congruent. Side is congruent to itself. Right angles are congruent. ANSWER Name the congruent triangles formed by the bridge cables. Explain how you know they are congruent. CB = CD AC AC = = ACB ACD ACB ACD = by Side - Angle - Side.
  17. 17. GUIDED PRACTICE for Example 3 Determine whether the triangles are congruent. 5. Yes, SAS ANSWER
  18. 18. GUIDED PRACTICE for Example 3 Determine whether the triangles are congruent. 6. Not Necessarily ANSWER
  19. 19. <ul><li>Assignment: P. 429 #1-12, 19-23 </li></ul>

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