6.4/6.5 ASA, AAS, HL and Applying Congruence

1. 6.4/6.5 ASA, AAS, HL and Applying Congruence Learning Objective: to prove that triangles are congruent using ASA, AAS, and HL, and to use corresponding parts of congruent triangles. Warm-up (IN) Constructed response practice

2. There are several short constructed-response items in CSAP, each taking approximately 3 to 5 minutes to complete.  Each short constructed-response item receives a single score of 0,1,or 2 points. 2 Points The response accomplishes the prompted purpose and effectively communicates the student's mathematical understanding.  The student's strategy and execution meet the content (including concepts, technique, representations, and connections), thinking processes, and qualitative demands of the task.  Minor omissions may exist, but do not detract from the correctness of the response.  1 Point The response partially accomplishes the prompted purpose.  The student's strategy and execution lack adequate evidence of the learning and strategic tools that are needed to accomplish the task.  The response may show some effort to accomplish the task, but with little success.  It is clear that the student requires additional feedback and/or instruction from the teacher in order to accomplish the task. O Points The response lacks evidence of mathematical knowledge that is appropriate to the intent of the task.

3. Learning Objective: to prove that triangles are congruent using ASA, AAS, and HL, and to use corresponding parts of congruent triangles. A B C D E F Notes Angle-Side-Angle (ASA) Postulate - If 2 angles and the included side of one triangle are congruent to 2 angles and the included side ofanother triangle, then the triangles are congruent

4. Learning Objective: to prove that triangles are congruent using ASA, AAS, and HL, and to use corresponding parts of congruent triangles. E D F G H Statements Reasons EX 1 –

5. Learning Objective: to prove that triangles are congruent using ASA, AAS, and HL, and to use corresponding parts of congruent triangles. A B C D E F Angle-Angle-Side (AAS) Theorem - If 2 angles and a non-included side of one triangle are congruent to 2 angles and a non-included sideof another triangle, then the triangles are congruent

6. Learning Objective: to prove that triangles are congruent using ASA, AAS, and HL, and to use corresponding parts of congruent triangles. A B C D E F Hypotenuse-Leg (HL) Theorem - If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a legof another right triangle, then the triangles are congruent

7. Learning Objective: to prove that triangles are congruent using ASA, AAS, and HL, and to use corresponding parts of congruent triangles. P M O N Statements Reasons EX 2 –

8. Learning Objective: to prove that triangles are congruent using ASA, AAS, and HL, and to use corresponding parts of congruent triangles. A B Definition of Congruent Triangles - Corresponding parts of congruent triangles are congruent CPCTC! Perpendicular Bisector Theorem - If a point is on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment

9. Learning Objective: to prove that triangles are congruent using ASA, AAS, and HL, and to use corresponding parts of congruent triangles. Statements Reasons F EX 3 – G E H

10. CKC p. 309!!

11. Out – Describe a method for proving that a part of one triangle is congruent to a part of another triangle. POW!! Summary – What I struggled with the most today was… HW – p. 303 # 1-9, 13 p. 309 #1-6, 8, 9