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Geometry
5-3, 5-5 &
5-6 Proving
Triangles
POINTS,
LINES AND
PLANESCongruent by
SAS, SSS, HL, ASA & AAS
What is required to show that
two triangles are congruent.
Learning Objective: Students will be able to prove
that two triangles are congruent.
Learning Target 5D I can read and write two column
proofs involving Triangle Congruence.
Triangle Congruence Theorems
Notes:
Page 135
of Student
Journal
(Students
take notes
on journal)
Geometry
POINTS, LINES AND PLANES
ABC  DEF by SAS
DB " F  DEF by SAS
Notes:
Page 135 of Student Journal
(Students take notes on
journal under theorem 5.5)
Click here to play video on how to
solve this problem.
Notes:
Page 145 of Student Journal
(Students take notes on journal on Vocabulary)
The legs of a right
triangle are
adjacent to the
right angle.
Geometry
LINES AND PLANES
Theorem POINTS,
5.8 Side-Side-Side
(SSS) Congruence
If three sides of one triangle are congruent to three
sides of second triangle, then the two triangles are
congruent.
ABC  DEF by SSS
DB " F  DEF by SSS
Notes:
Page 145 of Student Journal
(Students take notes on journal
under theorem 5.8)
Click here to play video on how to
solve this problem.
Geometry
POINTS, LINES AND PLANES
Theorem 5.9 Hypotenuse-Leg (HL) Congruence
If the hypotenuse and a leg of a right triangle are
congruent to the hypotenuse and a leg of a second right
triangle, then the two triangles are congruent.
ABC  DEF by HL
Notes:
Page 145 of Student Journal
(Students take notes on journal
under Theorem 5.9)
Click here to play video on how to
solve this problem.
POINTS, LINES AND PLANES
ABC  DEF by ASA
DB " F  DEF by ASA
Notes:
Page 150 of Student Journal
(Students take notes on journal
under Theorem 5.10)
Click here to play video on how to
solve this problem.
POINTS, LINES AND PLANES
Notes:
Page 150 of Student Journal
(Students take notes on journal
under Theorem 5.11)
Click here to play video on how to
solve this problem.
Use the AAS Congruence theorem to prove
that the triangles are congruent.
Reasons for
explaining
how you
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Given
Reflexive property of congruence
Symmetric property of congruence
Transitive property of =
Segment addition postulate
Angle addition postulate
Addition property of =
Subtraction property of =
Division property of =
Multiplication property of =
Substitution
Simplify
Distributive property of =
All right angles are congruent
Vertical angles are congruent
Definition of perpendicular lines
Definition of parallel lines
Definition of supplementary angles
Definition of complementary angles
Definition of midpoint
Definition of angle bisector
Definition of right triangles
Definition of isosceles triangles
Definition of equilateral triangles
Isosceles triangle theorem (ITT)
If lines are parallel then … alternate interior angles are congruent.
If lines are parallel then … Alternate exterior angles are congruent
If lines are parallel then … Corresponding angles are congruent
If lines are parallel then … Same side interior angles are supplementary
SSS, SAS, ASA, AAS, HL, CPCTC