text: Chapter 4
  
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  # Chapter 4 - PowerPoint PPT Presentation
  
  Chapter 4 . 4-6 Triangle congruence: ASA, AAS and HL. Objectives. Apply ASA, AAS, and HL to construct triangles and to solve problems. Prove triangles congruent by using ASA, AAS, and HL. . Compass.
  
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  ## Chapter 4
  
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  Presentation Transcript
  
  ### Chapter 4
  
  4-6 Triangle congruence: ASA, AAS and HL
  
  Objectives
  
  Apply ASA, AAS, and HL to construct triangles and to solve problems.
  
  Prove triangles congruent by using ASA, AAS, and HL.
  
  Compass
  • 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.
  Included Side
  • An included side is the common side of two consecutive angles in a polygon. The following postulate uses the idea of an included side.
  Solving Application
  • A 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?
  Example 1
  • Determine 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.
  
  Example 2
  • Determine if you can use ASA to prove NKL  LMN. Explain.
  
  By the Alternate Interior Angles Theorem. KLN  MNL. NL  LN by the Reflexive Property. No other congruence relationships can be determined, so ASA cannot be applied.
  
  Student Guided practice
  • Do problems 4 and 5 in your book page 264
  AAS Postulate
  • You can use the Third Angles Theorem to prove another congruence relationship based on ASA. This theorem is Angle-Angle-Side (AAS).
  Example 4
  • Use AAS to prove the triangles congruent.
  • Given: X  V, YZW  YWZ, XY  VY
  • Prove:  XYZ  VYW
  Example 5
  • Use AAS to prove the triangles congruent.
  • Given: JL bisects KLM, K  M
  • Prove: JKL  JML
  Student guided practice
  • Do problem 6 in your book page 264
  Example 6
  • Determine if you can use the HL Congruence Theorem to prove the triangles congruent. If not, tell what else you need to know.
  
  According to the diagram, the triangles are right triangles that share one leg.
  
  It is given that the hypotenuses are congruent, therefore the triangles are congruent by HL.
  
  Example 6
  
  This conclusion cannot be proved by HL. According to the diagram, the triangles are right triangles and one pair of legs is congruent. You do not know that one hypotenuse is congruent to the other.
  
  Student guided practice
  • Do problems 7 and 8 in your book page 264
  Homework
  • Do problems 11-17 in your book page 265
  Closure
  • Today we saw about congruence triangles
  • Next class we are going to continue with congruence and we are going to learn about CPCTC
explanation: The document is a PowerPoint presentation transcript from Chapter 4, focusing on triangle congruence using the ASA, AAS, and HL theorems. It includes definitions, examples, and student practice problems. The text contains multiple questions and answers related to proving triangle congruence.
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  # Chapter 4 - PowerPoint PPT Presentation
  
  Chapter 4 . 4-6 Triangle congruence: ASA, AAS and HL. Objectives. Apply ASA, AAS, and HL to construct triangles and to solve problems. Prove triangles congruent by using ASA, AAS, and HL. . Compass.
  
  I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
  
  ## Chapter 4
  
  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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
  
  - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
  Presentation Transcript
  
  ### Chapter 4
  
  4-6 Triangle congruence: ASA, AAS and HL
  
  Objectives
  
  Apply ASA, AAS, and HL to construct triangles and to solve problems.
  
  Prove triangles congruent by using ASA, AAS, and HL.
  
  Compass
  • 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.
  Included Side
  • An included side is the common side of two consecutive angles in a polygon. The following postulate uses the idea of an included side.
  Solving Application
  • A 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?
  Example 1
  • Determine 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.
  
  Example 2
  • Determine if you can use ASA to prove NKL  LMN. Explain.
  
  By the Alternate Interior Angles Theorem. KLN  MNL. NL  LN by the Reflexive Property. No other congruence relationships can be determined, so ASA cannot be applied.
  
  Student Guided practice
  • Do problems 4 and 5 in your book page 264
  AAS Postulate
  • You can use the Third Angles Theorem to prove another congruence relationship based on ASA. This theorem is Angle-Angle-Side (AAS).
  Example 4
  • Use AAS to prove the triangles congruent.
  • Given: X  V, YZW  YWZ, XY  VY
  • Prove:  XYZ  VYW
  Example 5
  • Use AAS to prove the triangles congruent.
  • Given: JL bisects KLM, K  M
  • Prove: JKL  JML
  Student guided practice
  • Do problem 6 in your book page 264
  Example 6
  • Determine if you can use the HL Congruence Theorem to prove the triangles congruent. If not, tell what else you need to know.
  
  According to the diagram, the triangles are right triangles that share one leg.
  
  It is given that the hypotenuses are congruent, therefore the triangles are congruent by HL.
  
  Example 6
  
  This conclusion cannot be proved by HL. According to the diagram, the triangles are right triangles and one pair of legs is congruent. You do not know that one hypotenuse is congruent to the other.
  
  Student guided practice
  • Do problems 7 and 8 in your book page 264
  Homework
  • Do problems 11-17 in your book page 265
  Closure
  • Today we saw about congruence triangles
  • Next class we are going to continue with congruence and we are going to learn about CPCTC
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a PowerPoint presentation transcript from Chapter 4, focusing on triangle congruence using the ASA, AAS, and HL theorems. It includes definitions, examples, and student practice problems. The text contains multiple questions and answers related to proving triangle congruence.
  
  Label: multiple-question-and-answer