ON HALF SHEET: Write the formula that was used in the video for today. Warm Up ON HALF SHEET: Write the formula that was used in the video for today.

Section 3.8- The HL Postulate

Why Do You Need To Know This? Let’s say you need to prove triangles congruent - what postulates can you use? SSS, SAS, ASA or AAS But suppose there is not enough information for any of those! Now you’re stuck right? .....WRONG! The Hypotenuse Leg Postulate is another method of proving triangles congruent 

What is the HL Postulate? HL Postulate: If there exists a correspondence between the vertices of two right triangles such that the hypotenuse and a leg of one triangle are congruent to the corresponding parts of the other triangle, the two right triangles are congruent. Or for short, (HL)

How and When to Use It ∆PLD  ∆FUN The HL Postulate only works with right triangles. When used in a proof, you must first establish the two are right triangles. Then, you get the legs and hypotenuses congruent and you’re done! N P ∆PLD  ∆FUN D L F U

Sample Problem D E F A B C Statements Reasons 1. AB ┴ BC 1. Given 2. DE ┴ EF 2. Given 3. AB DE 3. Given 4. AC DF 4. Given 5. ABC and  DEF are right  s 5. ┴ Lines form right  s 6. If a triangle has one right , then it is a right triangle 6. ∆ABC and ∆DEF are right triangles 7. ∆ABC  ∆DEF 7. HL ( 3, 4, 6) Given: AB ┴ BC DE ┴ EF AB DE AC DF Prove: ∆ABC  ∆DEF