4.3 Proving Triangles are Congruent: SSS and SAS – PART 2

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

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.

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

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

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.

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

SSS postulate SAS postulate

T C

S G

The vertex of the included angle is the point in common.

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SSS postulate

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SSS postulate

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SAS postulate SAS postulate