Problem 8 · 2012 Math Kangaroo
Easy
Geometry & Measurement
careful-counting
One vertex of the triangle on the left is connected to one vertex of the triangle on the right using a straight line so that no connecting line segment dissects either of the two triangles into two parts. In how many ways is this possible?
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Answer: D — 4
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Hint 1 of 2
Try joining each corner of the left triangle to each corner of the right triangle.
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Hint 2 of 2
Keep only the joins whose straight segment stays outside both triangles.
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Approach: test each vertex pairing
- There are 3 × 3 = 9 ways to pick one corner from each triangle and join them with a straight segment.
- A join is allowed only when the segment does not pass through the inside of either triangle.
- Checking the pairings, exactly 4 of the connecting segments avoid both triangles' interiors.
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