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Proving Congruence SSS, SAS

Chapter 4 Section 4

Learning Goal: Proving congruent triangles by SAS and SSS

Life is more accurately measured in the lives that you touch than

in the things you acquire

Why do we study Triangles

Architecture

Art

Sports

truss bridge

house trusses

tesselations

video

analysis

Congruence of Triangles--SSS

Notice the Corresponding Parts

∆ABC ∆ZXY ~=~=

Using SSS in proofs

E I

F H

First Draw your picture. . .

G ???

E

I F

H G

Prove: ΔFEG ΔHIG

Using SSS in proofs

E

I F

H G Prove: ΔFEG ΔHIG

Using SSS in proofs

1. Given

Statements

Prove: ΔFEG ΔHIG

3. SSS 3. ΔFEG ΔHIG

2. Def. of Midpoint 2.

1.

EI FH ~=~=

E

I F

H G

Proving Triangle Congruence

Reasons Proof:

Statements

3. SSS 3. ΔABG ΔCBG

1. Given 1.

2. _________ 2.

Congruence of Triangles -- SAS

Notice the parts correspond ∆ABC ∆FDE ~=~=

The angle is in the middle

and . . .

Congruence of Triangles -- SAS

Does the angle have to be in the middle?

4

3 5 3 4

A S S Watch out if it’s

not in the

middle Hyperlink to Geometry Chapter 4 ppt slide 148

C:\Program Files\07 GEOM TX IC\07GEOM Chapter 04.ppt

Coordinate Geometry

Use the Distance Formula to show that the corresponding sides are congruent.

Determine whether ΔWDV ΔMLP for D(–5, –1), V(–1, –2), W(–7, –4), L(1, –5), P(2, –1), and M(4, –7). Explain

There is a Shortcut

Use Rise over Run and right triangles to

prove the distance is equal !!! It’s actually

SAS

Triangle Congruence

Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible.

SSS

Triangle Congruence

Which postulate, if any, can be used to prove that the triangles are congruent?

SAS

Triangle Congruence

Which postulate, if any, can be used to prove that the triangles are congruent?

Not possible

Congruence in Right Triangles

15 15

7 7

HL – Hypotenuse Leg Triangles ~=~=Given:

A B

C

X Y

Z

Homework

Pages 230-232; #10, 15-18 all, 28, 31, 33, 35, 36-40(even), Copy the ∆ and do 44-49

(18 problems)

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