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Congruent Triangles

Congruent Triangles. Helpful websites. http://www.regentsprep.org/Regents/mathb/1c/preprooftriangles.htm http://www.mathwarehouse.com/geometry/congruent_triangles/ http://www.cliffsnotes.com/WileyCDA/CliffsReviewTopic/Congruent-Triangles.topicArticleId-18851,articleId-18788.html.

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Congruent Triangles

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  1. Congruent Triangles

  2. Helpful websites • http://www.regentsprep.org/Regents/mathb/1c/preprooftriangles.htm • http://www.mathwarehouse.com/geometry/congruent_triangles/ • http://www.cliffsnotes.com/WileyCDA/CliffsReviewTopic/Congruent-Triangles.topicArticleId-18851,articleId-18788.html

  3. 4-1 Congruent Figures Objective: To recognize congruent figures and their corresponding parts

  4. Vocabulary/ Key Concept • Congruent polygons- two polygons are congruent if their corresponding sides and angles are congruent • If two angles in a triangle are congruent to two angles in another triangle, then the third angles are congruent.

  5. Each pair of polygons are congruent. Find the measure of each numbered angle • M1 = 110 • m 2 = 120 • M3 = 90 • m 4 = 135

  6. WXYZ  JKLM. List 4 pairs of congruent sides and angles. • WX  JK • XY  KL • YZ  LM • ZW MJ • W  J • K  X • Y  L • Z  M

  7. Determine if the polygons are congruent. Explain. 1.G  I , GJH  IJH, 2.GHJ  IHJ 3. JI GJ, GH  IH, 4. JH  JH GHJ and IHJ are congruent because all corresponding angle and sides are congruent 1.Given –congruent markings 2.If two angles in a triangle are congruent to two angles in another triangle, then the third angles are congruent. 3.Given-congruent markings 4.Reflexive

  8. Determine if the polygons are congruent. Explain. 1.Q  T 2.QSR  TSV 3.R  V No, the triangles do no have corresponding sides that are congruent 1.Given – congruent measures 2.Vertical angles 3. If two angles in a triangle are congruent to two angles in another triangle, then the third angles are congruent.

  9. PROOF Statement 1. LM  QP LN QN MN  PN  L  Q 2.  LNM  QNP 3. P  M 4. LMN  QPN Reasons • GIVEN • VEERITCAL ANGLES • If two angles in a triangle are congruent to two angles in another triangle, then the third angles are congruent • 4. Def. of congruent polygons

  10. 4-2 Congruent Triangles by SSS and SAS Objective: To prove two triangles are congruent using SSS and SAS Postulates

  11. Key Concepts • SSS – Side-side-side corresponding congruence. • SAS – Side-Angle-Side corresponding Congruence. ANGLE MUST BE IN BETWEEN THE TWO SIDE

  12. Determine if you can use SSS or SAS to prove two triangles are congruent. Write the congruence statement. AB  CB --CONGRUENCE MARKING BD  BD -- REFLEXIVE ABD  CBD–CONGRUENCE MARKING  ABD   CBD by SAS

  13. Determine if you can use SSS or SAS to prove two triangles are congruent. Write the congruence statement. What do you know? NP = QP -- CONGRUENT MARKS NR = QR -- CONGRUENT MARKS RP = RP -- REFLEXIVE PROPERTY OF   PRN  PRQ by SSS

  14. Determine if you can use SSS or SAS to prove two triangles are congruent. Write the congruence statement. EM  PQ EN  PR CONGRUENCE MARKING N  R Not possible

  15. Proof Statements • AB  DC, BAC  DCA • AC  CA • ABC  CDA Reasons • Given • Reflexive property of  • SAS A B D C

  16. Try: Write a proof. Statement • EF GF, HF  DF •  DFE  HFG •  DFE   HFG Reasons • Given • Vertical angles • SAS

  17. 4-3 Congruent Triangles by AAS and ASA Objective: To prove two triangles are congruent using AAS and ASA Postulates

  18. Key Concepts • ASA – Two angles and an included side. • AAS – Two angles and a non-included side. SIDE IS IN BETWEEN THE ANGLES

  19. Determine if you can use ASA or AAS to prove two triangles are congruent. Write the congruence statement. TUV VST by ASA not possible BCEDCF by AAS

  20. Write a Proof Statement • KL ML,  K  M •  JLK   PLM •  JKL  PML Reasons • Given • Vertical angles • ASA

  21. What did you learn today? • What are some simple steps to writing proofs? • What are the four ways to prove triangles are congruent?

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