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

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.

SSS postulateSAS postulate

SSS postulate

Not enough info

SSS postulateSAS postulate

Not Enough InfoSAS postulate

SSS postulate

Not Enough Info

SAS postulate SAS postulate