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The diagram below is made up of two equilateral triangles and two parallelograms - Junior Cycle Mathematics - Question 6 - 2019

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The diagram below is made up of two equilateral triangles and two parallelograms. Three angles are marked. (a) Write the correct letter in each space in the table b... show full transcript

Worked Solution & Example Answer:The diagram below is made up of two equilateral triangles and two parallelograms - Junior Cycle Mathematics - Question 6 - 2019

Step 1

Write the correct letter in each space in the table below to show what type of angle each one is.

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Answer

The types of angles are as follows:

  • Angle K: Acute
  • Angle M: Reflex
  • Angle N: Obtuse

Step 2

Work out the size of each of the angles K, M, and N.

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Answer

Since the triangles are equilateral:

  • K=60 \angle K = 60^\circ
  • M=120 \angle M = 120^\circ
  • N=240 \angle N = 240^\circ

Step 3

Give a reason why the two triangles are similar.

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Answer

Both triangles are equilateral and all their corresponding angles are equal, making them similar.

Step 4

Give a reason why the two triangles are not congruent.

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Answer

Congruent triangles are the same size, and these two triangles are not equivalent in size.

Step 5

Use this information to construct the diagram in the space below.

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Answer

  1. Draw the smaller triangle with sides of length 4 cm.
  2. Draw the larger triangle with sides of length 8 cm, ensuring it is similar to the smaller triangle.
  3. Mark all corresponding angles and sides clearly to show the construction.

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