Question 23
How can the tangram pieces be rearranged to form each of the following figures?
The tangram puzzle uses seven specific geometric shapes.
Step 1 — Identify the Tangram Pieces
Let us call the two large right triangles LT1 and LT2. Let us call the medium right triangle MT. Let us call the two small right triangles ST1 and ST2. Let us call the square SQ. Let us call the parallelogram PG.
Step 2 — Arrange Pieces for Each Figure
We will describe how to arrange these seven pieces for each figure. Each description specifies the placement and orientation of each piece.
Answer
(i) Letter C: LT1 forms the bottom horizontal bar. Its right angle points bottom-left. LT2 forms the top horizontal bar. Its right angle points top-left. SQ is placed vertically in the middle. It connects LT1 and LT2. MT is placed above the Square. It forms the upper inner curve. ST1 is placed below the Square. It forms the lower inner curve. PG is placed to the right of MT. It forms the outer top arm. ST2 is placed to the right of ST1. It forms the outer bottom arm.
(ii) Pinwheel: The central square void is empty. LT1 forms the top-right blade. Its right angle points towards the center. ST1 completes the top-right blade. Its right angle points towards the center. LT2 forms the bottom-left blade. Its right angle points towards the center. ST2 completes the bottom-left blade. Its right angle points towards the center. MT forms the bottom-right blade. Its right angle points towards the center. PG forms the top-left blade. Its acute angle points towards the center.
(iii) Cat: LT1 forms the lower body. Its right angle points down-left. LT2 forms the upper body. Its right angle points up-left. ST1 forms the head. It is on top-left of LT2. ST2 forms the ear. It is on top-right of ST1. MT forms the front leg. It is below the front of LT1. SQ forms the back leg. It is below the back of LT1. PG forms the tail. It is at the back of LT1, pointing up.
(iv) Duck/Bird: LT1 forms the lower body. Its right angle points down-left. LT2 forms the upper body/wing. Its right angle points up-left. MT forms the head. It is at the front of LT2. ST1 forms the beak. It is at the front of MT. PG forms the tail. It is at the back of LT1, pointing up. SQ forms the upper leg. It is below LT1. ST2 forms the foot. It is below the Square.
(v) Running Man: LT1 forms the torso. Its right angle points down-left. LT2 forms the upper body. Its right angle points up-left. SQ forms the head. It is on top of LT2. MT forms an arm. It extends from LT2, pointing up-right. PG forms the front leg. It extends from LT1, pointing forward. ST1 forms the back leg. It extends from LT1, pointing down-left. ST2 forms the foot. It is at the end of ST1, pointing down-left.
(vi) Letter M: LT1 forms the left outer leg. Its right angle points down-left. LT2 forms the right outer leg. Its right angle points down-right. SQ forms the top middle. It is between LT1 and LT2. MT forms the left inner slant. It is below the left of SQ. PG forms the right inner slant. It is below the right of SQ. ST1 forms the bottom-left point. It is below MT. ST2 forms the bottom-right point. It is below PG.
(vii) Bat/Monster: LT1 forms the top-left point. Its right angle points up-left. LT2 forms the top-right point. Its right angle points up-right. SQ forms the upper body. It is between LT1 and LT2. MT forms the middle body. It is below the Square. ST1 forms the bottom-left jaw/leg. It is below the left of MT. ST2 forms the bottom-right jaw/leg. It is below the right of MT. PG forms the bottom jaw/tail. It connects ST1 and ST2.
(viii) Whale: LT1 forms the main body. Its right angle points down-left. LT2 forms the upper body. Its right angle points up-left. MT forms the upper tail fin. It is at the back of LT2. PG forms the lower tail fin. It is at the back of LT1. SQ forms the head. It is at the front of LT1. ST1 forms the upper fin. It is on top of the Square. ST2 forms the lower fin. It is below the Square.
(ix) Fish: LT1 forms the main body. Its right angle points down-left. LT2 forms the upper body. Its right angle points up-left. MT forms the head. It is at the front of LT1. PG forms the upper tail fin. It is at the back of LT2. ST1 forms the lower tail fin. It is at the back of LT1. SQ forms the upper fin. It is on top of LT2. ST2 forms the lower fin. It is below LT1.
(x) Face: LT1 forms the back of the head. Its right angle points down-left. LT2 forms the top of the head. Its right angle points up-left. SQ forms the forehead/eye. It is at the front of LT2. MT forms the nose. It is below the Square. PG forms the mouth. It is below the Medium Triangle. ST1 forms the chin. It is below the Parallelogram. ST2 forms the neck. It is below LT1.
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Hint 2: We can draw the whole line if any two of its points are known.]
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