Page 150 - Mathematics_Form_3

Circles

Activity 5.11: Deducing the property Theorem 5.7 is described geometrically
of parallel chords of a circle as follows.
In Figure 5.18, QYS and PXR are
Individually or in a group, perform the congruent arcs intercepted by the
following tasks:
FOR ONLINE READING ONLY
parallel chords, PQ and RS.
1. Cut a circle of a convenient radius
Y
from a manila paper.
Q S
2. Draw two parallel chords on the
circle.
3. Mark the arcs formed between the
two parallel chords.
4. Fold the circle along a chord which
joins the opposite ends of the two P R
X
chords.
5. Study the lengths of the arcs Figure 5.18: Parallel chords
between the parallel chords and
In Figure 5.18, Theorem 5.7 implies that
write a general statement regarding
the arcs PXR and QYS are congruent
your observation.
or equal.
6. Use the previous knowledge of
circle theorems, congruence and Properties of equal chords of a circle
similarity or algebra to prove your In the previous section, you learnt that
conclusion in task 5. parallel chords intercept congruent arcs.

7. Share your findings with the rest Given some conditions, such chords may
of the class members through be equal. In this case, equal chords of a
presentation. circle have unique properties.

In Activity 5.11, you realized that the
Activity 5.12: Deducing the
arcs formed between parallel chords
properties of equal chords of Mathematics for Secondary Schools
have the same measure. Congruent
a circle
arcs are arcs with the same measure.
Congruent arcs can be formed between
parallel chords of a circle. Individually or in a group, perform the
following tasks:

Theorem 5.7 1. Use a pair of compasses to draw a
Parallel chords of a circle intercept circle of a convenient radius centred
congruent arcs. at O.

Student\s Book Form Three 143

18/09/2025 09:59:47
MATHEMATIC F3 SB.indd 143 18/09/2025 09:59:47
MATHEMATIC F3 SB.indd 143