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The diagram below is made up of two equilateral triangles and two parallelograms - Junior Cycle Mathematics - Question 6 - 2019
Question 6
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. Use each letter only once.
Answer
For angle K, it is an Acute angle; therefore, write 'A'. For angle M, it is an Obtuse angle; therefore, write 'O'. For angle N, it is a Reflex angle; therefore, write 'R'.
| Type | Acute | Reflex | Obtuse |
|---|---|---|---|
| Angle | A | R | O |
Step 2
Work out the size of each of the angles K, M, and N.
Answer
Since both triangles are equilateral, we know that each angle measures 60 degrees. Therefore:
- The remaining angle must be calculated as follows: Since the total sum of angles in a triangle is 180° and we already have two angles of 60°, thus .
Step 3
Step 4
Step 5
Use this information to construct the diagram in the space below. Show clearly any construction lines used.
Answer
To construct the diagram:
- Draw an equilateral triangle with sides of 4 cm.
- From each vertex of this triangle, measure outwards twice the side length to construct a larger triangle with sides of 8 cm.
- Ensure that both triangles share the same angles and are drawn proportionately.