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Geometry 4.4 and 4.5 Triangle Congruence: SSS, SAS, ASA, AAS, and HL
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Geometry 4.4 and 4.5Triangle Congruence: SSS, SAS, ASA, AAS,
and HL
Learning TargetsStudents should be able to…
Apply SSS, SAS, ASA, AAS, and HL to construct triangles and to solve problems
Prove triangles congruent by using SSS, SAS, ASA, AAS, and HL.
Warm-up #1
Homework Check
Homework Check
Homework Check
Homework Check
4.1 – 4.3 Quiz
VocabularyTerm Name Diagram Additional
Notes
Included angle -an angle formed by two adjacent sides of a polygon
A B
C
VocabularyTerm Name Diagram Additional
Notes
Included angle -an angle formed by two adjacent sides of a polygon
Included side
Q
-a common side of two consecutive angles in a polygon.
A B
C
R Q
P
Postulate 4-4-1 Side-Side-Side (SSS)
Postulate Hypothesis Conclusion
If 3 sides of one triangle are congruent to 3 sides of another triangle, then the triangles are congruent.
A
B
C
F
D
E
Postulate 4-4-2 Side-Angle-Side (SAS)
Postulate Hypothesis Conclusion
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle , then the triangles are congruent.
A
B
C
F
D
E
Postulate 4-4-3 Angle-Side-Angle (ASA)
Postulate Hypothesis Conclusion
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
A
B
C
F
D
E
Postulate 4-4-4 Angle-Angle-Side (AAS)
Postulate Hypothesis Conclusion
If two angles and a nonincluded side of one triangle are congruent to the corresponding angles and nonincluded side of another triangle, then the triangles are congruent.
A
B
C
F
D
E
Review of Right Triangle Vocabulary
A
B C
Leg
Leg
Hypotenuse
Right Angle
Postulate 4-5-3 Hypotenuse-Leg (HL)
Postulate Hypothesis Conclusion
If the hypotenuse and a leg of a right triangle are congruent to a hypotenuse and a leg of another right triangle, then the triangles are congruent.
A
B
C
F
D
E
Proof TimeGiven: , Prove:
A D
B
C D
Statements Reasons
Proof TimeGiven:
M is the midpoint of Prove:
B C
MD F
Statements Reasons
On your own!
Re-teach (Extra Problems if needed)4-4
Re-teach (Extra Problems if needed)4-4
Re-teach (Extra Problems if needed)4-4
Re-teach (Extra Problems if needed)4-4
Re-teach (Extra Problems if needed)4-5
Re-teach (Extra Problems if needed)4-5
Re-teach (Extra Problems if needed)4-5
Re-teach (Extra Problems if needed)4-5
