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Learning Math Home
Geometry Session 3: Solutions
 
Session 3 Part A Part B Part C Homework
 
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A B C
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Solutions for Session 3, Part A

See solutions for Problems: A1 | A2 | A3 | A4


Problem A1

The first two shapes are not polygons because they are not made of straight line segments. The third shape is not a polygon because it is not closed, while the fourth shape divides the plane into three regions, rather than two.

<< back to Problem A1


 

Problem A2

There are 13 polygons. They are as follows:

 

Four small triangles, each defined by one side of the rectangle and two halves of the diagonals (e.g., XYV)

 

Four pentagons, each a complement of one of the small triangles (e.g., VYZWX)

 

Four large triangles, each defined by two sides of the rectangle and one of the diagonals (e.g., triangle XZW)

 

The rectangle XYZW

Score: (8 • 3) + (1 • 4) + (4 • 5) = 48 points

<< back to Problem A2


 

Problem A3

There are 13 polygons. They are as follows:

 

Four small rectangles, all of which share the vertex Q (e.g., SMPQ)

 

Four hexagons, each a complement of one of the small rectangles (e.g., PNOLSQ)

 

Four larger rectangles, each defined by two small rectangles sharing one side (e.g., MNTS)

 

The rectangle MNOL

Score: (9 • 4) + (4 • 6) = 60 points

<< back to Problem A3


 

Problem A4

There are 13 polygons. They are as follows:

 

Two small triangles (RUV and TWV)

 

Their two complements (hexagons VUSTQR and VWQRST)

 

Two quadrilaterals (RQWV and TSUV)

 

Their two complements (pentagons VRSTW and VTQRU)

 

Two larger triangles (RQT and TSR)

 

Three rectangles (RUWQ, USTW, and QRST)

Score: (4 • 3) + (5 • 4) + (2 • 5) + (2 • 6) = 54 points

<< back to Problem A4

 

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