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Here are two identical tiles - OCR - GCSE Maths - Question 10 - 2018 - Paper 1

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Here are two identical tiles. Sketch two quadrilaterals that can be made by joining the tiles. Write the mathematical name of each quadrilateral. Quadrilateral 1: ... show full transcript

Worked Solution & Example Answer:Here are two identical tiles - OCR - GCSE Maths - Question 10 - 2018 - Paper 1

Step 1

Sketch two quadrilaterals that can be made by joining the tiles.

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Answer

To create the quadrilaterals using the given tiles, we can form two shapes:

  1. Quadrilateral 1: A kite by connecting the two tiles along one of the longer sides. This results in two triangles that share the same base.
  2. Quadrilateral 2: A rectangle by aligning the tiles such that their angles match up, forming a perfect rectangle with sides of equal length.

Both quadrilaterals can be represented visually as follows:

  • Quadrilateral 1: Kite
  • Quadrilateral 2: Rectangle

Step 2

Work out the interior angles of each triangle.

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Answer

For Triangle 1:

  • Given angles: 60° and 30°.
  • The sum of angles in a triangle is always 180°: 180°−(60°+30°)=90°180° - (60° + 30°) = 90°
  • Therefore, Triangle 1 has angles of 60°, 30°, and 90°.

For Triangle 2:

  • Given angles: 60° and 30° (the tiles can create the same angles when joined differently).
  • Again, using the sum of angles: 180°−(60°+30°)=90°180° - (60° + 30°) = 90°
  • Thus, Triangle 2 has angles of 60°, 30°, and 90°.

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