Download Congruence in Right Triangles

CONGRUENCE IN RIGHT TRIANGLES
Right Triangles
hypotenuse
•The side opposite the
right angle is the longest
side and is called the
hypotenuse.
•The other two sides are
called legs.
legs
Theorem 4-6 Hypotenuse-Leg (HL) Theorem
If the hypotenuse and a leg of one right
triangle are congruent to the hypotenuse and a
leg of another right triangle, then the triangles
are congruent.
Y
B
ABC  XYZ
A
C
X
Z
Why?
DGF  DEF
What additional information do you need to prove the
triangles congruent by HL?
When proving triangles are congruent by
HL, the following conditions must be met:
•The hypotenuses are congruent.
•At least one set of legs is congruent.
•You have two right triangles.
Since BC ≅AD,
<ABC and <DBC are right
angles.
C
Since <ABC and <DBC are
right angles,
Then ΔABC and Δ DBC are
right triangles.
A
B
D
Statements
Reasons
Statements
Reasons
HOMEWORK
P. 219
5 - 10, 14 - 15,
WRITE AS A PROOF: 28 - 29