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Mastering Congruence Proofs with ASA and AAS Criteria

Learn the Angle-Side-Angle and Angle-Angle-Side criteria for proving triangle congruence. Understand how to apply these postulates, write proofs, and analyze geometric figures. Develop skills in making, testing, and justifying conjectures in coordinate geometry. Enhance your ability to establish properties and relationships of geometric objects with counterexamples and reasoning methods. Complete assignments to reinforce learning.

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Mastering Congruence Proofs with ASA and AAS Criteria

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  1. Lesson 4-5 Proving Congruence – ASA, AAS

  2. Ohio Content Standards:

  3. Ohio Content Standards: Describe and apply the properties of similar and congruent figures; and justify conjectures involving similarity and congruence.

  4. Ohio Content Standards: Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects.

  5. Ohio Content Standards: Use coordinate geometry to represent and examine the properties of geometric figures.

  6. Ohio Content Standards: Prove or disprove conjectures and solve problems involving two- and three-dimensional objects represented within a coordinate system.

  7. Ohio Content Standards: Analyze two-dimensional figures in a coordinate plane; e.g., use slope and distance formulas to show that a quadrilateral is a parallelogram.

  8. Ohio Content Standards: Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.

  9. Ohio Content Standards: Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects.

  10. Ohio Content Standards: Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof.

  11. Included Side

  12. Included Side The side of a triangle that is between two angles.

  13. Postulate 4.3

  14. Postulate 4.3 Angle-Side-Angle Congruence

  15. Postulate 4.3 If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. Angle-Side-Angle Congruence

  16. Write a proof.

  17. Write a proof. R E L W D

  18. Theorem 4.5

  19. Theorem 4.5 Angle-Angle-Side Congruence

  20. Theorem 4.5 If two angles and the nonincluded side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent. Angle-Angle-Side Congruence

  21. Write a proof.

  22. Write a proof. K J L M N

  23. Assignment:Pgs. 211-213 10-18 evens, 36-41 all

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