Download Lesson 4.4 4.5 NOTES

Geometry Chapter 4-4/4-5 notes
Proving Triangles Congruent
Lesson 4-4/4-5 OBJECTIVE:
SWBAT use the SSS, SAS & ASA Postulates and the AAS & HL Theorems to test and prove triangle congruence. What do you think? - Is it always necessary to prove all 6 parts of
two triangles are congruent in order to prove that the triangles
are congruent?
In this lesson we will learn all
that will prove two triangles are
congruent and by the end of the lesson you will be able to answer the above question.
Side-Side-Side Congruence Postulate: If the sides of one triangle are congruent
to the sides of a second triangle, then the triangles are congruent.
Abbreviation:
Triangle Congruence: Δ ABC ≅ Δ Side-Angle-Side Congruence Postulate: 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.
Abbreviation:
Triangle Congruence: Δ ABC ≅ Δ Angle-Side-Angle Congruence Postulate: 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.
Abbreviation:
Triangle Congruence: Δ ABC ≅ Δ Angle-Angle-Side Theorem: If two angles and a non-included side of one triangle
are congruent to the corresponding two angles and side of a second triangle, then the
triangles are congruent.
Abbreviation:
Triangle Congruence: Δ ABC ≅ Δ Hypotenuse-Leg Theorem: If the hypotenuse and a leg of one right triangle are
congruent to the hypotenuse and the corresponding leg of another triangle, then the
triangles are congruent.
Abbreviation:
State which congruence method(s) can be used to prove the triangles congruent.
If no method applies, write none.
Refer to the diagram at the right and
name the sides of ∆ABC for which ∠B
is the included angle.
We now know 5 methods of proving two triangles congruent, they are:
SSS - (side-side-side)
SAS - (side-angle-side)
AAS - (angle-angle-side)
ASA - (angle-side-angle)
HL - (hypotenuse leg)
*it MUST be a right triangle