Download 4.3-‐4.5 Proving Triangles are Congruent

4.3-­‐4.5 Proving Triangles are Congruent
Side-Side-Side (SSS) Theorem:
If all 3 sides are congruent, then the
2 triangles are congruent.
Decide whether the triangles are congruent. Explain your reasoning.
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Side-Angle-Side (SAS) Postulate:
If 2 sides and the included angle
are congruent, then both triangles
are congruent.
2
Angle-Side-Angle Theorem:
If 2 angles and the included side are
congruent, then the 2 triangles are
congruent.
Angle-Angle-Side Theorem:
If 2 consecutive angles, followed by a
side are congruent, then the 2 triangles
are congruent.
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Hypotenuse-Leg Theorem:
In a right triangle if the corresponding
hypotenuse and leg are congruent, then
the 2 triangles are congruent.
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You may not use the following to prove 2
triangles are congruent!!
1. "Angle,Angle, Angle or A.A.A": No calling triple A for help!
2. "Angle, Side, Side or A.S.S": No Swearing!
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Decide whether the 2 triangles are congruent. If they are, tell why.
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Decide whether the 2 triangles are congruent. If so, tell why.
a.
b.
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Decide whether the 2 triangles are congruent. If so, tell why.
a.
b.
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Overlapping triangles are when the 2 triangles share a common
side or angle.
Example: 1
Keys to solve overlapping triangles!
1. Use 2 colored pencils to outline
the 2 triangles.
2. Redraw each triangle individually
and label all angles and sides with given
information.
3. Look at the 2 triangles and see if you
can prove that they are congruent using:
SAS, SSS, ASA, AAS, or HL
T
Z
V
X Y
W
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Try two more! Are they congruent??
a.
b.
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