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Proving Congruence SSS, SAS - CISD · 2013-12-03 · Proving Congruence SSS, SAS Chapter 4 Section...

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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
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Page 1: Proving Congruence SSS, SAS - CISD · 2013-12-03 · Proving Congruence SSS, SAS Chapter 4 Section 4 Learning Goal: Proving congruent triangles by SAS and SSS Life is more accurately

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

Page 2: Proving Congruence SSS, SAS - CISD · 2013-12-03 · Proving Congruence SSS, SAS Chapter 4 Section 4 Learning Goal: Proving congruent triangles by SAS and SSS Life is more accurately

Why do we study Triangles

Architecture

Art

Sports

truss bridge

house trusses

tesselations

video

analysis

Page 3: Proving Congruence SSS, SAS - CISD · 2013-12-03 · Proving Congruence SSS, SAS Chapter 4 Section 4 Learning Goal: Proving congruent triangles by SAS and SSS Life is more accurately

Congruence of Triangles--SSS

Notice the Corresponding Parts

∆ABC ∆ZXY ~=~=

Page 4: Proving Congruence SSS, SAS - CISD · 2013-12-03 · Proving Congruence SSS, SAS Chapter 4 Section 4 Learning Goal: Proving congruent triangles by SAS and SSS Life is more accurately

Using SSS in proofs

E I

F H

First Draw your picture. . .

G ???

E

I F

H G

Prove: ΔFEG ΔHIG

Page 5: Proving Congruence SSS, SAS - CISD · 2013-12-03 · Proving Congruence SSS, SAS Chapter 4 Section 4 Learning Goal: Proving congruent triangles by SAS and SSS Life is more accurately

Using SSS in proofs

E

I F

H G Prove: ΔFEG ΔHIG

Page 6: Proving Congruence SSS, SAS - CISD · 2013-12-03 · Proving Congruence SSS, SAS Chapter 4 Section 4 Learning Goal: Proving congruent triangles by SAS and SSS Life is more accurately

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

Page 7: Proving Congruence SSS, SAS - CISD · 2013-12-03 · Proving Congruence SSS, SAS Chapter 4 Section 4 Learning Goal: Proving congruent triangles by SAS and SSS Life is more accurately

Proving Triangle Congruence

Reasons Proof:

Statements

3. SSS 3. ΔABG ΔCBG

1. Given 1.

2. _________ 2.

Page 8: Proving Congruence SSS, SAS - CISD · 2013-12-03 · Proving Congruence SSS, SAS Chapter 4 Section 4 Learning Goal: Proving congruent triangles by SAS and SSS Life is more accurately

Congruence of Triangles -- SAS

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

The angle is in the middle

and . . .

Page 10: Proving Congruence SSS, SAS - CISD · 2013-12-03 · Proving Congruence SSS, SAS Chapter 4 Section 4 Learning Goal: Proving congruent triangles by SAS and SSS Life is more accurately

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

Page 11: Proving Congruence SSS, SAS - CISD · 2013-12-03 · Proving Congruence SSS, SAS Chapter 4 Section 4 Learning Goal: Proving congruent triangles by SAS and SSS Life is more accurately

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

Page 12: Proving Congruence SSS, SAS - CISD · 2013-12-03 · Proving Congruence SSS, SAS Chapter 4 Section 4 Learning Goal: Proving congruent triangles by SAS and SSS Life is more accurately

Triangle Congruence

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

SAS

Page 13: Proving Congruence SSS, SAS - CISD · 2013-12-03 · Proving Congruence SSS, SAS Chapter 4 Section 4 Learning Goal: Proving congruent triangles by SAS and SSS Life is more accurately

Triangle Congruence

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

Not possible

Page 14: Proving Congruence SSS, SAS - CISD · 2013-12-03 · Proving Congruence SSS, SAS Chapter 4 Section 4 Learning Goal: Proving congruent triangles by SAS and SSS Life is more accurately

Congruence in Right Triangles

15 15

7 7

HL – Hypotenuse Leg Triangles ~=~=Given:

A B

C

X Y

Z

Page 15: Proving Congruence SSS, SAS - CISD · 2013-12-03 · Proving Congruence SSS, SAS Chapter 4 Section 4 Learning Goal: Proving congruent triangles by SAS and SSS Life is more accurately

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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