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
(a) 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.
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Angle
Type
K
Acute
M
Obtuse
N
Reflex
Step 2
(b) Work out the size of each of the angles K, M, and N. Remember that the two triangles are equilateral.
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
The angles of an equilateral triangle are all equal to 60°.
Thus:
∣K∣=60°
Since the sum of angles in a triangle is 180°, if angle K is 60°, the remaining angles M and N have the following relation:
∣M∣+∣K∣+∣N∣=180°
By the properties of angles in triangles, ∣M∣=120° and ∣N∣=240°.
Step 3
(c) (i) Give a reason why the two triangles are similar.
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Both triangles are equilateral and have all their corresponding angles equal, which means they satisfy the Angle-Angle (AA) criterion for similarity.
Step 4
(c) (ii) Give a reason why the two triangles are not congruent.
98%
120 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Congruent triangles must have equal size as well as equal angles, and these two are not the same size.
Step 5
(d) Use this information to construct the diagram in the space below. Show clearly any construction lines used.
97%
117 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To construct the triangles:
Draw a triangle with sides of length 4 cm (small triangle).
Using the same angles as the small triangle, draw a larger triangle with sides of 8 cm, ensuring that the angles remain the same.
Clearly label the height, base, and vertices to denote construction lines, if necessary.
Join the Junior Cycle students using SimpleStudy...
