By: Eric Onofrey Tyler Julian Drew Kuzma. Let’s say you need to prove triangles congruent But...
-
Upload
melvin-brown -
Category
Documents
-
view
212 -
download
0
Transcript of By: Eric Onofrey Tyler Julian Drew Kuzma. Let’s say you need to prove triangles congruent But...
SECTION 3.8- THE HL POSTULATE
By: Eric OnofreyTyler JulianDrew Kuzma
Why Do You Need To Know This?
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
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
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!
Sample ProblemA
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
Practice Problem #1 Statements1.F is the midpoint of AD 2. 3. 4.
5. <EFA, < EFD are rt <s6. Triangle EFD and triangle
EFA are right triangles7. Triangle EFD is congruent
to triangle EFA8. <AEF is congruent to <
DEF
Reasons1. Given 2. Given3. Given4. If a pt if a midpoint of a seg,
then it divides the seg into 2 congruent segs.
5. Perpendicular lines form rt <s6. 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
EDEAADEF
EDEAADEF FDAF
Practice Problem #2
Statements1. ABCD is a rectangle2. AC is congruent to BD
3. AB is congruent to DC
4. <ABC, <DCB are right5. Triangle ABC, Triangle
DCB are right triangles6.Triangle ABC is
congruent to triangle DCB
7. <EBC is congruent to < ECB
8. Triangle BEC is an isosceles triangle
Reasons1. Given2. Rectangle implies diagonals
congruent3. Rectangle implies opposite
sides congruent4. 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
Practice Problem #3
Statements1. ABDE is a rectangle
2.
3.
4.<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 <DEC8. <BAE, < DEA are right <s9. <BAE is congruent to <DEA
10. <CAE is congruent to <CEA
Reasons
1. Given2. Given
3. Rectangle implies opposite sides congruent
4. Rectangle implies right <s5. If a triangle has one right
< then it is a right triangle
6. HL (2,3, 5)
7. CPCTC8. Rectangle implies right <s9. Right angles are
congruent10. Subtraction
A E
B C D Given: ABDE is a
rectangle
ECAC
Prove: <AEC is congruent to < EAC
ECAC
EDAB
Practice Problem #4
Statements1. ABCD is a square2. BD Bisects AC
3.
4.5.
6. <BEC, < AED are right <s
7. Triangle BEC and triangle AED are right triangles
8. Triangle BEC is congruent to triangle AED
Statements1. Given2. 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
ECAE
BDAC
ADBC
Practice Problem #5
Statements1.Circle D2. BD is an altitude of
Triangle ABC3. 4. <ADB, <CDB are right <s
5. Triangle ADB and triangle CDB are right triangles
6. 7. Triangle ADB is congruent
to triangle CDB
Reasons1. Given2. Given
3. Given4. 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
BGiven: Circle D
BD is an altitude of triangle ABC
Prove: Triangle ABD is congruent to triangle CBD
BCAB
BCAB
DCAD
Practice Problem #6
Statements1. Circle A2. 3. 4. <ACB, <ACD are right <s
5, Triangle ABC, triangle ADC are right triangles
6. 7. Triangle ABC is congruent
to triangle ADC
Reasons1. Given2. Given3. Given4. Perpendicular lines
form right <s5. 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
BDAC
BDAC CDBC
CDBC
ADAB
Works Cited
CliffsNotes.com. Congruent Triangles. 18 Jan 2011<http://www.cliffsnotes.com/study_guide/topicArticleId-18851,articleId-18788.html>.
"Geometry: Congruent Triangles - CliffsNotes." Get Homework Help with CliffsNotes Study Guides - CliffsNotes. Web. 18 Jan. 2011. <http://www.cliffsnotes.com/study_guide/Congruent-Triangles.topicArticleId-18851,articleId-18788.html>.