5. Perimeter = 31  NPO = 50   CED = 55  DE = 11 PO = 33 UV = 36

6.  CED = 37  Perimeter = 40 DE = 18 LM = 22

7. REVIEW OF RIGHT TRIANGLES

8. TRIANGLE CONGRUENCES

9. ASA (ANGLE-SIDE-ANGLE) POSTULATE If two angles and the included side in one triangle are congruent to two angles and the included side in another triangle, then the two triangles are congruent.

10. PRACTICE In each pair below, the triangles are congruent. Tell which triangle congruence postulate allows you to conclude that they are congruent, based on the markings in the figures.

11. AAS (ANGLE-ANGLE-SIDE) POSTULATE If two angles and a nonincluded side of one triangle are congruent to the corresponding angles and nonincluded side of another triangle, then the triangles are congruent.

12. PRACTICE Which pairs of triangles below can be proven to be congruent by the AAS Congruence Theorem?

13. THREE OTHER POSSIBILITIES AAA combination—three angles Does it work? SSA combination—two sides and an angle that is not between them (that is, an angle opposite one of the two sides.)

14. SPECIAL CASE OF SSA When you try to draw a triangle for an SSA combination, the side opposite the given angle can sometimes pivot like a swinging door between two possible positions. This “swinging door” effect shows that two triangles are possible for certain SSA information.

15. A SPECIAL CASE OF SSA If the given angle is a right angle, SSA can be used to prove congruence. In this case, it is called the Hypotenuse-Leg Congruence Theorem.

16. HL (HYPOTENUSE-LEG) CONGRUENCE THEOREM If the hypotenuse and a leg of a right triangle are congruent to the Hypotenuse and a leg of another right triangle, then the two triangles are congruent.

17. OTHER RIGHT TRIANGLE THEOREMS LL (LEG-LEG) Congruence Theorem If the two legs of a right triangle are congruent to the corresponding two legs of another right triangle, then the triangles are congruent. LA (LEG-ANGLE) Congruence Theorem If a leg and an acute angle of a right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent.

18. OTHER RIGHT TRIANGLE THEOREMS HA (HYPOTENUSE-ANGLE) Congruence Theorem If the hypotenuse and an acute angle of a right triangle are congruent to the corresponding hypotenuse and acute angle of another triangle, then the triangles are congruent. HL (HYPOTENUSE-LEG) Congruence Theorem If the hypotenuse and a leg of a right triangle are congruent to the corresponding hypotenuse and leg of another right triangle, then the triangles are congruent.

19. PRACTICE Determine whether each pair of triangles can be proven congruent. If so, write a congruence statement and name the postulate or theorem used. 1. 3. 5. 2. 4. 6.

20. WARM UP Determine whether each pair of triangles can be proven congruent. If so, write a congruence statement and name the postulate or theorem used. 8. 10. 7. 9.