By: Eric Onofrey Tyler Julian Drew Kuzma

 Let’s say you need to prove triangles congruent  But there is not enough information to use SAS, ASA, or SSS.  Now you’re stuck right?.....WRONG!  The Hypotenuse Leg Postulate is another method of proving triangles congruent

 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)

 The HL Postulate only works with right triangles.  When used in a proof, you must establish the two are right triangles.  So after you do that, you get the legs and hypotenuses congruent and you’re done!

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

Statements 1.F is the midpoint of AD <EFA, < EFD are rt <s 6. Triangle EFD and triangle EFA are right triangles 7. Triangle EFD is congruent to triangle EFA 8. <AEF is congruent to < DEF Reasons 1. Given 2. Given 3. Given 4. If a pt if a midpoint of a seg, then it divides the seg into 2 congruent segs. 5. Perpendicular lines form rt <s 6. If a triangle has one right <, then it is right 7. HL (2, 4, 6) 8. CPCTC E A F D B C Given: F is the midpoint of AD Prove: <AEF congruent to < DEF

Statements 1. ABCD is a rectangle 2. AC is congruent to BD 3. AB is congruent to DC 4. <ABC, <DCB are right 5. Triangle ABC, Triangle DCB are right triangles 6.Triangle ABC is congruent to triangle DCB 7. <EBC is congruent to < ECB 8. Triangle BEC is an isosceles triangle Reasons 1. Given 2. Rectangle implies diagonals congruent 3. Rectangle implies opposite sides congruent 4. Rectangle implies right angles 5. If a triangle has one right angle, then it is right. 6. HL (2,3 5,) 7. CPCTC 8. If two <s are congruent then the triangle is isosceles. A D E B C Given: ABCD is a rectangle Prove: Triangle BEC is an isosceles triangle

Statements 1. ABDE is a rectangle <ABC, < EDC are right <s 5.Triangle ABC, triangle EDC are right triangles 6.Triangle ABC is congruent to triangle EDC 7.<BAC is congruent to <DEC 8. <BAE, < DEA are right <s 9. <BAE is congruent to <DEA 10. <CAE is congruent to <CEA Reasons 1. Given 2. Given 3. Rectangle implies opposite sides congruent 4. Rectangle implies right <s 5. If a triangle has one right < then it is a right triangle 6. HL (2,3, 5) 7. CPCTC 8. Rectangle implies right <s 9. Right angles are congruent 10. Subtraction A E B C D Given: ABDE is a rectangle Prove: <AEC is congruent to < EAC

Statements 1. ABCD is a square 2. BD Bisects AC <BEC, < AED are right <s 7. Triangle BEC and triangle AED are right triangles 8. Triangle BEC is congruent to triangle AED Statements 1. Given 2. Square implies diagonals bisect 3. If a seg is bisected, then it is divided into 2 congruent segs 4. Square implies sides congruent 5. Square implies diagonals perpendicular 6. Perpendicular lines form right <s 7. If a triangle has one right < then it is a right triangle 8. HL (3, 4, 7) A E B D C Given: ABCD is a square Prove: Triangle AED is congruent to triangle BEC

Statements 1.Circle D 2. BD is an altitude of Triangle ABC <ADB, <CDB are right <s 5. Triangle ADB and triangle CDB are right triangles Triangle ADB is congruent to triangle CDB Reasons 1. Given 2. Given 3. Given 4. If a seg is an altitude, then it is drawn from a triangle vertex and forms right <s with the opposite side. 5. If a triangle has one right <, then it is a right triangle 6. All radii of a circle are congruent. 7. HL (3, 5, 6) A D C B Given: Circle D BD is an altitude of triangle ABC Prove: Triangle ABD is congruent to triangle CBD

Statements 1. Circle A <ACB, <ACD are right <s 5, Triangle ABC, triangle ADC are right triangles Triangle ABC is congruent to triangle ADC Reasons 1. Given 2. Given 3. Given 4. Perpendicular lines form right <s 5. If a triangle has one right <, then it is a right triangle 6. All radii of a circle are congruent 7. HL( 2, 5, 6) B C D A Given: Circle A Prove: Triangle ABC is congruent to triangle ADC

 CliffsNotes.com. Congruent Triangles. 18 Jan  "Geometry: Congruent Triangles - CliffsNotes." Get Homework Help with CliffsNotes Study Guides - CliffsNotes. Web. 18 Jan