(a) (i) Construct the triangle ABC, where |AB| = 10 cm, |∠CAB| = 60° and |∠ABC| = 40°. Label each vertex clearly. (ii) Measure |BC|, and write your answer in cm, correct to 1 decimal place. (b) The diagram shows a parallelogram with vertices P, Q, R, and S. |∠SPQ| = 115°, |∠QRS| = α° and |∠RSP| = β°. (i) Write down the value of α and the value of β. (ii) Explain why the triangle PQR is congruent to triangle RSP. Give a reason for any statement you make in your explanation.

Leaving Cert Mathematics Trigonometry: (a) (i) Construct the triangle A

(a) (i) Construct the triangle ABC, where |AB| = 10 cm, |∠CAB| = 60° and |∠ABC| = 40° - Leaving Cert Mathematics - Question 6 - 2018

Question 6

(a) (i) Construct the triangle ABC, where |AB| = 10 cm, |∠CAB| = 60° and |∠ABC| = 40°. Label each vertex clearly. (ii) Measure |BC|, and write your answer in cm, co... show full transcript

Worked Solution & Example Answer:(a) (i) Construct the triangle ABC, where |AB| = 10 cm, |∠CAB| = 60° and |∠ABC| = 40° - Leaving Cert Mathematics - Question 6 - 2018

Step 1

Construct the triangle ABC, where |AB| = 10 cm, |∠CAB| = 60° and |∠ABC| = 40°. Label each vertex clearly.

96%

114 rated

Answer

Start by drawing a line segment |AB| of 10 cm.
At point A, use a compass to draw an angle of 60° to create the line |AC|.
At point B, draw another angle of 40° to create the line |BC|.
Extend lines |AC| and |BC| until they intersect at point C.
Label the vertices clearly as A, B, and C.

Step 2

Measure |BC|, and write your answer in cm, correct to 1 decimal place.

99%

104 rated

Answer

Using a ruler, measure the length of line segment |BC|. After measurement, you find |BC| = 8 cm.

Step 3

Write down the value of α and the value of β.

96%

101 rated

Answer

Given that |∠SPQ| = 115°,

Since the opposite angles in a parallelogram are equal, we have:
- α = 115°
The sum of angles in a triangle equals 180°, thus:
- β = 180° - |∠SPQ| = 180° - 115° = 65°.

Step 4

Explain why the triangle PQR is congruent to triangle RSP.

98%

120 rated

Answer

The triangles PQR and RSP are congruent due to the following reasons:

Both triangles share side |PR|, which is common to both triangles.
The angles |∠PQR| and |∠RSP| are equal to 65°.
Lastly, |QR| = |PS| because they are opposite sides of the parallelogram.

Thus, by the Side-Angle-Side (SAS) congruence criterion, triangle PQR is congruent to triangle RSP.

(a) (i) Construct the triangle ABC, where |AB| = 10 cm, |∠CAB| = 60° and |∠ABC| = 40° - Leaving Cert Mathematics - Question 6 - 2018

Worked Solution & Example Answer:(a) (i) Construct the triangle ABC, where |AB| = 10 cm, |∠CAB| = 60° and |∠ABC| = 40° - Leaving Cert Mathematics - Question 6 - 2018

Construct the triangle ABC, where |AB| = 10 cm, |∠CAB| = 60° and |∠ABC| = 40°. Label each vertex clearly.

Measure |BC|, and write your answer in cm, correct to 1 decimal place.

Write down the value of α and the value of β.

Explain why the triangle PQR is congruent to triangle RSP.

Join the Leaving Cert students using SimpleStudy...