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Understanding Triangle Congruence: ASA, AAS, and HL with Examples and Quizzes

This lesson focuses on triangle congruence, specifically the postulates and theorems: ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and HL (Hypotenuse-Leg). Students will learn about sides and angles in triangles, and how congruence can be proven using corresponding parts. The session includes detailed examples, practice problems, and a quiz to test understanding. Key concepts like vertical angles and the CPCTC (Corresponding Parts of Congruent Triangles are Congruent) theorem will be discussed to strengthen grasp on the subject.

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Understanding Triangle Congruence: ASA, AAS, and HL with Examples and Quizzes

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  1. 4-5 Triangle Congruence: ASA, AAS, and HL Holt Geometry Warm Up Lesson Presentation Lesson Quiz

  2. AC 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; hypotenuse Third s Thm.

  3. B is the included angle between sides AB and BC.

  4. Remember! SSS, SAS, ASA, AAS, and HL use corresponding parts to prove triangles congruent. CPCTC uses congruent triangles to prove corresponding parts congruent. CPCTCis an abbreviation for the phrase “Corresponding Parts of Congruent Triangles are Congruent.” It can be used as a justification in a proof after you have proven two triangles congruent.

  5. Check It Out! Example 1 A landscape architect sets up the triangles shown in the figure to find the distance JK across a pond. What is JK? One angle pair is congruent, because they are vertical angles. Two pairs of sides are congruent, because their lengths are equal.Therefore the two triangles are congruent by SAS. By CPCTC, the third side pair is congruent, so JK = 41 ft.

  6. 26° ABC  DBC BC  BC AB  DB So ∆ABC  ∆DBC by SAS Lesson Quiz: Part I 1. Show that∆ABC  ∆DBC, when x = 6. Which postulate, if any, can be used to prove the triangles congruent? 3. 2. none SSS

  7. Lesson Quiz: Part I Identify the postulate or theorem that proves the triangles congruent. HL ASA SAS or SSS

  8. Lesson Quiz: Part I Find each angle measure. 1. mR 2. mP Find each value. 3.x 4.y 5.x 28° 124° 6 20 26°

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