# 7.2.3 Geometrical Constructions, PT3 Focus Practice

Question 6:
Diagram below in the answer space shows part of a triangle ABC.

Answer:
(a)

Solution:
(a)

(b)
$\angle ACB={72}^{o}$

Question 7:
Diagram below shows a quadrilateral ABQR.

(a) Using only a ruler and a pair of compasses, construct the diagram using the measurement given.
Begin from the straight lines AB and BQ provided in the answer space.
(b) Based on the diagram constructed in (a), measure the length, in cm, of QR.

Answer:
(a)

Solution:
(a)

(b)
QR = 5.9 cm

# 7.2.2 Geometrical Constructions, PT3 Focus Practice

7.2.2 Geometrical Constructions, PT3 Focus Practice 2

Question 4:
Diagram below shows a parallelogram PQRS. The point T lies on PQ such that ST is perpendicular to PQ.

Using only a ruler and a pair of compasses, construct parallelogram PQRS, beginning from the lines PQ and PS provided in the answer space.

Answer
:

Solution
:

Question 5:
Diagram below shows a triangle ABC.

(a) Using only a ruler and a pair of compasses, construct triangle ABC, beginning with the straight line BC in the answer space.
(b)   Hence, measure the length, in cm, of BA.

Answer
:
(a)

Solution
:
(a)

(b)
BA = 4.5 cm

# 7.2.1 Geometrical Constructions, PT3 Focus Practice

7.2.1 Geometrical Constructions, PT3 Focus Practice
Question 1:
Diagram below in the answer space shows part of triangle ABC.
(a) Using a pair of compasses, a protractor and a ruler, draw a triangle ABC starting from the line given in the answer space with AB = 4.5 cm, BC = 6 cm and ∠ABC = 105o.
(b) Measure ∠BCA.

Answer
:
(a)

Solution
:
(a)

(b)
∠BCA = 31o

Question 2:
Diagram below shows a triangle ABC drawn not to scale.

Diagram in the answer space shows a straight line AB.
(a) Using only a ruler and a pair of compasses, construct
(i) triangle ABC to the measurements shown in diagram above,
(ii)   the perpendicular line to the straight line AC which passes through the point B.
(b)   Measure the perpendicular distance between straight line AC and point B.

Answer
:
(a)(i),(ii)

Solution
:
(a)(i),(ii)

(b)
5.3 cm

Question 3:
Diagram below shows a pentagon ABCDE.

Using only a ruler and a pair of compasses, construct the diagram, beginning from the straight lines CD and DE provided in the answer space.

Answer:

Solution: