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It’s the Final Project!4.1-4.4

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

R

E

F

X

REX= FEX

<R = <F

<FEX = <REX

<RXER = <FXE

RE = FE

RX = FX

EX= EX

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.

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.

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.

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.

You use CPCTC (after you have proved that the triangles are congruent) to prove that sides or angles of the triangles are also congruent.

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WX=YZ, WX=YZ GIVEN

WY=WY Reflexive

WXY WZY SSS

<X = <ZCPCTC

Now Its YOUR Turn

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.

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HINT: both sides are congruent

PRACTICE MAKES PERFECT

http://mdk12.org/share/clgtoolkit/lessonplans/MethodsofProofTwoColumnProofs.pdf

http://regentsprep.org/Regents/mathb/1c/preprooftriangles.htm

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/geometry/ch4notes.pdf

THE END :)