The diagram shows the rhombus QRST - Junior Cycle Mathematics - Question 9 - 2018
Question 9
The diagram shows the rhombus QRST.
It is a parallelogram in which all four sides are equal in length.
The diagonals cross at point K. Two of the angles are marked X... show full transcript
Worked Solution & Example Answer:The diagram shows the rhombus QRST - Junior Cycle Mathematics - Question 9 - 2018
Step 1
|QT| = |TS|
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Answer
In a rhombus, all sides are equal in length. Therefore, the lengths of segment QT and segment TS are equal.
Step 2
QST is an isosceles triangle
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Answer
Since QRST is a rhombus, triangles QST and RST are isosceles, as they share the common sides of the rhombus.
Step 3
|∠X| = |∠Y|
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By the properties of isosceles triangles, the angles opposite to equal sides are equal. Hence, |∠X| = |∠Y|.
Step 4
|QK| = |SK|
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The diagonals of a rhombus bisect each other, which means that |QK| is equal to |SK|.
Step 5
QKT is congruent to SKT
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By the SAS (Side Angle Side) postulate, the triangles QKT and SKT are congruent.
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