It

1
Its the Final Project!4.1-4.4

• By
• Jake Rothbaum
• Rachel Greenberg

2
Its 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!

3
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

4
Naming a Polygon

• A polygon, ABCDEF, can be changed.
• Names include
• BCDEFA
• CDEFAB
• DEFABC
• EFABCD
• FABCDE

E
REX FEX
F
R
X
RE FE RX FX EX EX
ltR ltF ltFEX ltREX ltRXER ltFXE
5
Now its YOUR Turn

• 1.) If ?CAT ?DOG, then complete (draw a
  picture first)
• MltC _____ ?TCA ? _____
• GD ? _____ ltO ? _____
• TA _____ ?ODG ? _____

6
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

AAS Angle- Angle- Side Theorem If two angles and
a non-included side of one triangle are congruent
to the corresponding angles and non-included side
of another triangle, then the triangles are
congruent.
SSS Side -Side -Side Postulate If the sides of
one triangle are congruent to the sides of
another triangle then those triangles are
congruent.
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.
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.
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.
7
Triangle Problems
8
CPCTC

• Corresponding Parts of a Congruent Triangle are
  Congruent.

You use CPCTC (after you have proved that the
triangles are congruent) to prove that sides or
angles of the triangles are also congruent.
WXYZ, WXYZ
GIVEN
WYWY
Reflexive
WXY WZY
SSS
CPCTC
ltX ltZ
9
Now Its YOUR Turn
10
Isosceles and Equilateral Triangles
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
11
PRACTICE MAKES PERFECT
http//mdk12.org/share/clgtoolkit/lessonplans/Meth
odsofProofTwoColumnProofs.pdf http//regentsprep.
org/Regents/mathb/1c/preprooftriangles.htm CHECK
THESE WEBSITES OUT FOR MORE PRACTICE
12

• The review questions are throughout the
  presentation after each section. Hope you enjoyed
  it. Good luck!

13
WORK CITED

• http//www.mrbrewer.net/files/geometry/ch4notes.pd
  f

14
THE END )