Transcript section 4.1-4.4 - Fulton County Schools

It’s the Final Project!
4.1-4.4
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By:
Jake Rothbaum
Rachel Greenberg
It’s the Introduction
• Hello everyone. Our names are Jake and
Rachel. We are here to teach yall about triangle
congruency!
• In this power point, you will learn about
congruent polygons, triangle congruency,
analyzing triangle congruency, and how to use
triangle congruency. Most importantly you will
learn how to do mind boggling proofs. Get
ready for your head to hurt!
Congruent Polygons
(a.k.a. 4.1)
• Polygon Congruence Postulate:
Polygons are congruent if and only if there
is a correspondence between their sides
and angles such that:
– Each pair of corresponding angles are
congruent
– Each pair of corresponding sides are
congruent
– Converse holds true as well
Naming a Polygon
• A polygon, ABCDEF,
can be changed.
• Names include:
– BCDEFA
– CDEFAB
– DEFABC
– EFABCD
– FABCDE
E
REX=
F
R
X
<R = <F
<FEX = <REX
<RXER = <FXE
RE = FE
RX = FX
EX= EX
FEX
Now its YOUR Turn
1.) If ΔCAT = ΔDOG, then complete: (draw a
picture first)
• M<C = _____ ΔTCA _____
• GD _____ <O _____
• TA = _____ ΔODG _____
Triangle
Congruence
(a.k.a. 4.2 & 4.3)
Q: How can we prove that two
triangles are congruent to
each other?
A: Five ways: SSS, SAS, ASA,
AAS, HL
SSS:
Side -Side -Side Postulate:
If the sides of one triangle are
congruent to the sides of another
triangle then those triangles are
congruent.
SAS
Side- Angle- Side Postulate:
If two side and the included angle in
the triangle are congruent to two
sides and the included angle in
another triangle, then the two
triangles are congruent.
AAS
Angle- Angle- Side
Theorem:
ASA
Angle-Side Angle
Postulate:
If two angles and the included
side of a triangle are congruent to
two other angles and an included
side of another triangle, then the
two triangles are congruent.
If two angles and a nonincluded side of one
triangle are congruent to
the corresponding angles
and non-included side of
another triangle, then the
triangles are congruent.
HL
Hypotenuse Leg
Theorem:
If the hypotenuse and a
leg of a right triangle are
congruent to the
hypotenuse and a leg of
another right triangle,
then the two triangles are
congruent.
Triangle Problems
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CPCTC
Corresponding Parts of a
Congruent Triangle are
Congruent.
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You use CPCTC (after you have proved that the triangles are congruent)
to prove that sides or angles of the triangles are also congruent.
WX=YZ, WX=YZ
GIVEN
WY=WY
Reflexive
WXY
<X = <Z
WZY
SSS
CPCTC
Now Its YOUR Turn
Isosceles and Equilateral
Triangles
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Isosceles Triangle Theorem: If two sides of a triangle are congruent, then the
angles opposite them (base angles) are congruent.
Converse of the Isosceles Triangle Theorem: If two angles (base angles) of
a triangle are congruent, then the sides opposite them are congruent.
Equilateral Triangles: measures of each angle are 60 degrees.
HINT: both sides are
congruent
PRACTICE MAKES
PERFECT
http://mdk12.org/share/clgtoolkit/lessonplans/MethodsofProof
TwoColumnProofs.pdf
http://regentsprep.org/Regents/mathb/1c/preprooftriangles.ht
m
CHECK THESE WEBSITES OUT FOR MORE PRACTICE
The review questions are
throughout the presentation after
each section. Hope you enjoyed it.
Good luck!
WORK CITED
http://www.mrbrewer.net/files/geo
metry/ch4notes.pdf
THE END :)