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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. Congruent Triangles in a Coordinate Plane. AC  FH. AB  FG. Use the SSS Congruence Postulate to show that  ABC   FGH. S OLUTION. AC = 3 and FH = 3. AB = 5 and FG = 5. Congruent Triangles in a Coordinate Plane. - PowerPoint PPT Presentation
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4.3 Proving Triangles are Congruent: SSS and SAS – PART 2
Transcript
Page 1: 4.3 Proving Triangles are Congruent: SSS and SAS –  PART 2

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

Page 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

Page 3: 4.3 Proving Triangles are Congruent: SSS and SAS –  PART 2

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.

Page 4: 4.3 Proving Triangles are Congruent: SSS and SAS –  PART 2

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

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

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

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

SSS postulate SAS postulate

Page 9: 4.3 Proving Triangles are Congruent: SSS and SAS –  PART 2

T C

S G

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

SSS postulateSAS postulate

Page 10: 4.3 Proving Triangles are Congruent: SSS and SAS –  PART 2

SSS postulate

Not enough info

Page 11: 4.3 Proving Triangles are Congruent: SSS and SAS –  PART 2

SSS postulateSAS postulate

Page 12: 4.3 Proving Triangles are Congruent: SSS and SAS –  PART 2

Not Enough InfoSAS postulate

Page 13: 4.3 Proving Triangles are Congruent: SSS and SAS –  PART 2

SSS postulate

Not Enough Info

Page 14: 4.3 Proving Triangles are Congruent: SSS and SAS –  PART 2

SAS postulate SAS postulate


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