1. UNIT 7: CONGRUENT TRIANGLES, AND THEOREMS Final Exam Review

2. TOPICS TO INCLUDE  Corresponding Sides and Angles  Congruent Triangles  Triangle Sum Theorem  Midsegment of a Triangle Theorem

3. CORRESPONDING SIDES AND ANGLES

5.  You Try: ∆ANT ≅ ∆BUG

6. CONGRUENT TRIANGLES  There are 5 postulates that can prove that 2 triangles are congruent  SSS  SAS  ASA  AAS  HL

7. CONGRUENT TRIANGLES  SSS (Side Side Side)  All 3 SIDES are congruent to each other  SAS (Side Angle Side)  2 SIDES and the INCLUDED angle are congruent to each other

8. CONGRUENT TRIANGLES  ASA (Angle Side Angle)  2 ANGLES and the INCLUDED side are congruent to each other  AAS (Angle Angle Side)  2 ANGLES and the NON-INCLUDED side are congruent to each other

9. CONGRUENT TRIANGLES  HL (Hypotenuse leg)  There must be a RIGHT angle  2 sides must be marked  The HYPOTENUSE  1 other LEG

10. CONGRUENT TRIANGLES  Determine how the triangles are congruent 1. 2. 3. 4. 5. 6.

11. TRIANGLE SUM THEOREM  The Triangle Sum Theorem states that the THREE angles in a triangle ALWAYS add up to 180°  Example: 82 + 43 + X = 180 125 + X = 180 X = 55° X

12. TRIANGLE SUM THEOREM  Now you try:

13. MIDSEGMENT OF A TRIANGLE THEOREM  The Midsegment of a Triangle Theorem states that the misdsegment of a triangle is equal to HALF of the THIRD side  BEFORE setting up an equation, MULTIPLY the midsegment by 2 and then solve.  Example: 2(5X – 1) = 58 10X – 2 = 58 10X = 60 X = 6

14. MIDSEGMENT OF A TRIANGLE THEOREM  Now you try:

15. ALL DONE