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Learning Math Home
Geometry Session 2: Solutions
 
Session 2 Part A Part B Part C Homework
 
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A B C 
Homework

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Solutions for Session 2, Part B

See solutions for Problems: B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 | B9


Problem B1

Here is the table filled in for the triangles with given lengths and for other sample triangles.

Side A

Side B

Side C

Is it a triangle?

Can it be deformed?

4

4

4

Yes

No

4

3

2

Yes

No

3

2

1

No

N/A

4

3

2

Yes

No

1

2

4

No

N/A

2

4

4

Yes

No

3

1

1

No

N/A

2

3

3

Yes

No

2

4

2

No

N/A

Other answers will vary individually, but no triangle will be deformable.

<< back to Problem B1


 

Problem B2

No, this is not possible. If we attach the two sides of lengths of 4 units to the endpoints of the side of length 10, the first two sides will not meet at a point to create a triangle. Together they are too short.

<< back to Problem B2


 

Problem B3

Three lengths can form a triangle only if the sum of the lengths of any two sides is greater than the length of the third side.

<< back to Problem B3


 

Problem B4

Yes. Because the sum of lengths of any two sides is greater than the length of the remaining side, the two sides will be able to meet at a point and create a triangle when attached to the endpoints of the third side.

<< back to Problem B4


 

Problem B5

No, three fixed lengths determine one and only one triangle. This is demonstrated by the fact that none of the triangles found in Problem B1 can be "deformed" into a different shape.

<< back to Problem B5


 

Problem B6

Here is the table filled in for the quadrilaterals with given lengths and other sample quadrilaterals.

Side A

Side B

Side C

Side D

Is it a quadri-
lateral?

Can it be deformed?

4

4

4

4

Yes

Yes

4

3

2

2

Yes

Yes

3

2

1

1

Yes

Yes

4

1

2

1

No

N/A

1

1

1

4

No

N/A

2

2

2

2

Yes

Yes

1

4

3

1

Yes

Yes

1

3

3

4

Yes

Yes

2

3

4

1

Yes

Yes

4

1

1

2

No

N/A

Other answers will vary individually, but all quadrilaterals will be deformable.

<< back to Problem B6


 

Problem B7

As long as no more than two sides of a quadrilateral are equal in length, we can reorder the way the sides are connected and obtain a different quadrilateral. This is not the case with triangles: If we reorder the sides, we get the same triangle.

<< back to Problem B7


 

Problem B8

Four lengths can form a quadrilateral as long as the sum of the lengths of any three sides is greater than the length of the fourth side.

<< back to Problem B8


 

Problem B9

Yes. For example:

Also, if the sides are not the same length, ordering them differently will produce different quadrilaterals.

<< back to Problem B9


 

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