proving congruence sss, sas - cisd · 2013-12-03 · proving congruence sss, sas chapter 4 section...
TRANSCRIPT
![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](https://reader030.vdocuments.mx/reader030/viewer/2022040222/5e47606ad4685d354e616437/html5/thumbnails/1.jpg)
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](https://reader030.vdocuments.mx/reader030/viewer/2022040222/5e47606ad4685d354e616437/html5/thumbnails/2.jpg)
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](https://reader030.vdocuments.mx/reader030/viewer/2022040222/5e47606ad4685d354e616437/html5/thumbnails/3.jpg)
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](https://reader030.vdocuments.mx/reader030/viewer/2022040222/5e47606ad4685d354e616437/html5/thumbnails/4.jpg)
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](https://reader030.vdocuments.mx/reader030/viewer/2022040222/5e47606ad4685d354e616437/html5/thumbnails/5.jpg)
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](https://reader030.vdocuments.mx/reader030/viewer/2022040222/5e47606ad4685d354e616437/html5/thumbnails/6.jpg)
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](https://reader030.vdocuments.mx/reader030/viewer/2022040222/5e47606ad4685d354e616437/html5/thumbnails/7.jpg)
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](https://reader030.vdocuments.mx/reader030/viewer/2022040222/5e47606ad4685d354e616437/html5/thumbnails/8.jpg)
Congruence of Triangles -- SAS
Notice the parts correspond ∆ABC ∆FDE ~=~=
The angle is in the middle
and . . .
![Page 9: 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](https://reader030.vdocuments.mx/reader030/viewer/2022040222/5e47606ad4685d354e616437/html5/thumbnails/9.jpg)
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
![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](https://reader030.vdocuments.mx/reader030/viewer/2022040222/5e47606ad4685d354e616437/html5/thumbnails/10.jpg)
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](https://reader030.vdocuments.mx/reader030/viewer/2022040222/5e47606ad4685d354e616437/html5/thumbnails/11.jpg)
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](https://reader030.vdocuments.mx/reader030/viewer/2022040222/5e47606ad4685d354e616437/html5/thumbnails/12.jpg)
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](https://reader030.vdocuments.mx/reader030/viewer/2022040222/5e47606ad4685d354e616437/html5/thumbnails/13.jpg)
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](https://reader030.vdocuments.mx/reader030/viewer/2022040222/5e47606ad4685d354e616437/html5/thumbnails/14.jpg)
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](https://reader030.vdocuments.mx/reader030/viewer/2022040222/5e47606ad4685d354e616437/html5/thumbnails/15.jpg)
Homework
Pages 230-232; #10, 15-18 all, 28, 31, 33, 35, 36-40(even), Copy the ∆ and do 44-49
(18 problems)