Download Lesson 4.5 ∆ ≅ ∆DEF by the HL postulate Theorem 4.5

GEOMETRY NOTES
Lesson 4.5
Prove Triangles Congruent by AAS and HL
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Key words: hypotenuse, leg of right triangle
Review for the Lesson
In a right triangle the sides adjacent to the right angle are called the legs.
The side opposite the right angle is called the hypotenuse.
hypotenuse
leg
leg
Lesson 4.5
State the theorem in your own words:
Theorem 4.5 - Hypotenuse – Leg (HL) 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 triangles are congruent.
B
E
C
A
F
D
∆‫∆ ≅ ܥܤܣ‬DEF
by the HL postulate
Prove the triangles congruent.
S
R
Statements
B
T
A
C
Reasons
Page 1
Theorem 4.6 – Angle-Angle-Side (AAS) Theorem
If two angles and the non-included side of one triangle
are congruent to two angles and the non-included angle
of another triangle, then the triangles are congruent.
B
A
E
C
D
F
∆‫∆ ≅ ܥܤܣ‬DEF by the AAS Theorem
Using the AAS and HL Theorems
C
P
തതതത
തതതത ∥ തതതത
‫ܤܥ‬, തതതത
ܲܳ ≅ ‫ܤܥ‬
Given: ܲܳ
Prove: ∆ܴܲܳ ≅ ∆BCR
R
B
Q
Steps for proving triangles congruent:
1) Mark the diagram with the given
information.
2) Look for other angles and sides that you can
show are congruent using vertical angles,
alternate interior angles, midpoints, angle
bisectors, definition of perpendicular, etc.
3) Figure out if you have SSS, SAS, AAS, HL, or
ASA.
4) If you are missing a side or angle, see if you
can figure out how to show the missing side or
angle congruent.
5) Write out the proof.
Statement
Reasons
Page 2