4.3 Proving Triangles are Congruent: SSS and SAS – PART 2
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Transcript of 4.3 Proving Triangles are Congruent: SSS and SAS – PART 2
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4.3 Proving Triangles are Congruent: SSS and SAS – PART 2
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Congruent Triangles in a Coordinate Plane
AC FH
AB FGAB = 5 and FG = 5
SOLUTION
Use the SSS Congruence Postulate to show that ABC FGH.
AC = 3 and FH = 3
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Congruent Triangles in a Coordinate Plane
d = (x 2 – x1 ) 2 + ( y2 – y1 )
2
= 3 2 + 5
2
= 34
BC = (– 4 – (– 7)) 2 + (5 – 0 )
2
d = (x 2 – x1 ) 2 + ( y2 – y1 )
2
= 5 2 + 3
2
= 34
GH = (6 – 1) 2 + (5 – 2 )
2
Use the distance formula to find lengths BC and GH.
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Congruent Triangles in a Coordinate Plane
BC GH
All three pairs of corresponding sides are congruent, ABC FGH by the SSS Congruence Postulate.
BC = 34 and GH = 34
![Page 5: 4.3 Proving Triangles are Congruent: SSS and SAS – PART 2](https://reader036.fdocuments.net/reader036/viewer/2022081418/56813c33550346895da5b124/html5/thumbnails/5.jpg)
Congruent Triangles in a Coordinate Plane
MN DE
PM FEPM = 5 and FE = 5
SOLUTION
Use the SSS Congruence Postulate to show that NMP DEF.
MN = 4 and DE = 4
![Page 6: 4.3 Proving Triangles are Congruent: SSS and SAS – PART 2](https://reader036.fdocuments.net/reader036/viewer/2022081418/56813c33550346895da5b124/html5/thumbnails/6.jpg)
Congruent Triangles in a Coordinate Plane
d = (x 2 – x1 ) 2 + ( y2 – y1 )
2
= 4 2 + 5
2
= 41
PN = (– 1 – (– 5)) 2 + (6 – 1 )
2
d = (x 2 – x1 ) 2 + ( y2 – y1 )
2
= (-4) 2 + 5
2
= 41
FD = (2 – 6) 2 + (6 – 1 )
2
Use the distance formula to find lengths PN and FD.
![Page 7: 4.3 Proving Triangles are Congruent: SSS and SAS – PART 2](https://reader036.fdocuments.net/reader036/viewer/2022081418/56813c33550346895da5b124/html5/thumbnails/7.jpg)
Congruent Triangles in a Coordinate Plane
PN FD
All three pairs of corresponding sides are congruent, NMP DEF by the SSS Congruence Postulate.
PN = 41 and FD = 41
![Page 8: 4.3 Proving Triangles are Congruent: SSS and SAS – PART 2](https://reader036.fdocuments.net/reader036/viewer/2022081418/56813c33550346895da5b124/html5/thumbnails/8.jpg)
SSS postulate SAS postulate
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T C
S G
The vertex of the included angle is the point in common.
SSS postulateSAS postulate
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SSS postulate
Not enough info
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SSS postulateSAS postulate
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Not Enough InfoSAS postulate
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SSS postulate
Not Enough Info
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SAS postulate SAS postulate