PQRSTU is a hexagon with all sides equal. Which of these statements is/are correct?

UQ = TR

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UQ = ST

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△

PUQ

≅

△

STR

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TR = PU

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Solution

The correct options are
A UQ = TR
C $△$ PUQ $≅$ $△$ STR
Since, PQRSTU is a hexagon with all sides equal,
i.e., PQ = QR = RS = ST = TU = UP
and $∠$ P = $∠$ Q = $∠$ R = $∠$ S = $∠$ T = $∠$ U

$∴$ In triangles, $△$ PUQ and $△$ STR
PQ = UP = RS = ST
and $∠$ P = $∠$ S
Hence, by SAS criterion for congruency of triangles
$△$ PUQ $≅$ $△$ STR

So, UQ = TR (corresponding parts of congruent triangles)

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Similar questions

Draw a hexagon with all sides equal, but not all angles equal.

Combine these two statements using, 'if and only if'

p:If a rectangle is a square, then all its four sides are equal.

q:If all the four sides of a rectangle are equal, then the rectangle is a square.

△ P Q T

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