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Advanced Geometry
Section 3.8 The HL Postulate
Learner Objective: Students will solve proofs and problems using
the HL Postulate of triangle congruence.
Warm Up
Statement
Reason
How can we prove that triangles are congruent?
What about SSA?
In these triangles, two pairs of corresponding sides and a NON-INCLUDED pair of corresponding angles are
congruent.
Do the triangles appear to be congruent?
There is one special case when SSA does prove triangles are congruent. This occurs when the
corresponding angles are RIGHT ANGLES which makes the congruent sides a HYPOTENUSE
and a LEG of the RIGHT triangle.
H-L 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,
then the two RIGHT TRIANGLES are congruent.
ONLY APPLIES TO RIGHT TRIANGLES!
STATEMENTS
Given:
Prove:
bisects
C
B
A
D
REASONS
Prove: Corresponding angle bisectors of congruent triangles are congruent.
STATEMENTS
E
B
A
G
C
D
Given:
bisects
bisects
Prove:
H
F
REASONS
HW:
Pg. 158
# 1,2,6,7,10,12,15