Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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.

 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.

 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.

 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.

 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.

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

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

 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.

 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.

 Problem B9 Yes. For example: Also, if the sides are not the same length, ordering them differently will produce different quadrilaterals.