4-4 Triangle Congruence: ASA, AAS Holt Geometry Warm Up Warm Up Lesson Presentation Lesson...

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Transcript of 4-4 Triangle Congruence: ASA, AAS Holt Geometry Warm Up Warm Up Lesson Presentation Lesson...

  • Warm UpLesson PresentationLesson Quiz

  • Warm Up

    1. What are sides AC and BC called? Side AB?

    2. Which side is in between A and C?

    3. Given DEF and GHI, if D G and E H, why is F I?

    legs; hypotenuseThird s Thm. 4.4 Congruent Triangles by ASA - AAS

  • Apply ASA and AAS construct triangles and to solve problems.

    Prove triangles congruent by using ASA and AAS. Objectives4.4 Congruent Triangles by ASA - AAS

  • included sideVocabulary4.4 Congruent Triangles by ASA - AAS

  • Participants in an orienteering race use a map and a compass to find their way to checkpoints along an unfamiliar course.Directions are given by bearings, which are based on compass headings. For example, to travel along the bearing S 43 E, you face south and then turn 43 to the east.4.4 Congruent Triangles by ASA - AAS

  • An included side is the common side of two consecutive angles in a polygon. The following postulate uses the idea of an included side.4.4 Congruent Triangles by ASA - AAS

  • 4.4 Congruent Triangles by ASA - AAS

  • Example 1: Problem Solving ApplicationA mailman has to collect mail from mailboxes at A and B and drop it off at the post office at C. Does the table give enough information to determine the location of the mailboxes and the post office?4.4 Congruent Triangles by ASA - AAS

  • The answer is whether the information in the table can be used to find the position of points A, B, and C.List the important information: The bearing from A to B is N 65 E. From B to C is N 24 W, and from C to A is S 20 W. The distance from A to B is 8 mi.4.4 Congruent Triangles by ASA - AAS

  • Draw the mailmans route using vertical lines to show north-south directions. Then use these parallel lines and the alternate interior angles to help find angle measures of ABC.4.4 Congruent Triangles by ASA - AAS

  • mCAB = 65 20 = 45mCAB = 180 (24 + 65) = 914.4 Congruent Triangles by ASA - AAS

  • One and only one triangle can be made using the information in the table, so the table does give enough information to determine the location of the mailboxes and the post office.4.4 Congruent Triangles by ASA - AAS

  • Check It Out! Example 1 What if? If 7.6km is the distance from B to C, is there enough information to determine the location of all the checkpoints? Explain.7.6kmYes; the is uniquely determined by AAS.4.4 Congruent Triangles by ASA - AAS

  • Example 2: Applying ASA CongruenceDetermine if you can use ASA to prove the triangles congruent. Explain.Two congruent angle pairs are give, but the included sides are not given as congruent. Therefore ASA cannot be used to prove the triangles congruent.4.4 Congruent Triangles by ASA - AAS

  • Check It Out! Example 2 Determine if you can use ASA to prove NKL LMN. Explain.4.4 Congruent Triangles by ASA - AAS

  • You can use the Third Angles Theorem to prove another congruence relationship based on ASA. This theorem is Angle-Angle-Side (AAS).4.4 Congruent Triangles by ASA - AAS

  • 4.4 Congruent Triangles by ASA - AAS

  • 4.4 Congruent Triangles by ASA - AAS

  • Example 3: Using AAS to Prove Triangles CongruentUse AAS to prove the triangles congruent.Given: X V, YZW YWZ, XY VYProve: XYZ VYW4.4 Congruent Triangles by ASA - AAS

  • Example 3: Using AAS to Prove Triangles Congruent4.4 Congruent Triangles by ASA - AASGiven (Angle) Given (Angle) Given (Side)By AAS1. X V2. YZW YWZ3. XY VY 4. JL=JL Reflexive Prop. (Side) KLJ = MLJ

    Given: X V, YZW YWZ, XY VY

    Statement Reason

  • 4.4 Congruent Triangles by ASA - AASWe can also prove the triangles are congruent by using a flow chart.

  • Check It Out! Example 3 Use AAS to prove the triangles congruent.Given: JL bisects KLM, K MProve: JKL JML4.4 Congruent Triangles by ASA - AAS

  • Example 3: Using AAS to Prove Triangle CongruenceGiven Given (Angle) Def. of Bisect (Angle)By AAS4.4 Congruent Triangles by ASA - AAS1. JL bisect
  • 4.4 Congruent Triangles by ASA - AASWe can also prove the triangles are congruent by using a flow chart.

  • Lesson Quiz: Part IIdentify the postulate or theorem that proves the triangles congruent.ASASAS or SSS4.4 Congruent Triangles by ASA - AAS2.

  • Lesson Quiz: Part II4. Given: FAB GED, ABC DCE, AC EC Prove: ABC EDC 4.4 Congruent Triangles by ASA - AAS

  • Lesson Quiz: Part II Continued4.4 Congruent Triangles by ASA - AAS

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