1. POINTS, LINES AND PLANES Learning Target 5D I can read and write two column proofs involving Triangle Congruence. Geometry 5-3, 5-5 & 5-6 Proving Triangles Congruent by SAS, SSS, HL, ASA & AAS Learning Objective: Students will be able to prove that two triangles are congruent.

2. Triangle Congruence Theorems Notes: Page 135 of Student Journal (Students take notes on journal)

3. POINTS, LINES AND PLANES Geometry

4. Notes: Page 135 of Student Journal (Students take notes on journal under theorem 5.5) Click here to play video on how to solve this problem.

5. The legs of a right triangle are adjacent to the right angle. Notes: Page 145 of Student Journal (Students take notes on journal on Vocabulary)

6. POINTS, LINES AND PLANES Geometry Theorem 5.8 Side-Side-Side (SSS) Congruence If three sides of one triangle are congruent to three sides of second triangle, then the two triangles are congruent.

7. Click here to play video on how to solve this problem. Notes: Page 145 of Student Journal (Students take notes on journal under theorem 5.8)

8. POINTS, LINES AND PLANES Geometry Theorem 5.9 Hypotenuse-Leg (HL) Congruence If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent. Do not use: AAA, SSA or ASS!

9. Click here to play video on how to solve this problem. Notes: Page 145 of Student Journal (Students take notes on journal under Theorem 5.9)

10. POINTS, LINES AND PLANES

11. Click here to play video on how to solve this problem. Notes: Page 150 of Student Journal (Students take notes on journal under Theorem 5.10)

12. POINTS, LINES AND PLANES Do not use: AAA, SSA or ASS! Do use: SAS, SSS, HL, ASA, AAS!

13. Click here to play video on how to solve this problem. Notes: Page 150 of Student Journal (Students take notes on journal under Theorem 5.11) Use the AAS Congruence theorem to prove that the triangles are congruent.

14. Reasons for explaining how you know: Given Reflexive property of congruence Symmetric property of congruence Transitive property of = Segment addition postulate Angle addition postulate Addition property of = Subtraction property of = Division property of = Multiplication property of = Substitution Simplify Distributive property of = All right angles are congruent Vertical angles are congruent Definition of perpendicular lines Definition of parallel lines Definition of supplementary angles Definition of complementary angles Definition of midpoint Definition of angle bisector Definition of right triangles Definition of isosceles triangles Definition of equilateral triangles Isosceles triangle theorem (ITT) If lines are parallel then … alternate interior angles are congruent. If lines are parallel then … Alternate exterior angles are congruent If lines are parallel then … Corresponding angles are congruent If lines are parallel then … Same side interior angles are supplementary SSS, SAS, ASA, AAS, HL, CPCTC