Page 143 - Mathematics_Form_3

Circles

Angle formed in a semicircle 9. Using the previous circle theorems,
A semicircle is half a circle and algebra, congruence and similarity
measures 180 .° Its end points are the theorems, prove the findings
end points of a diameter. The angle established in task 8.
inscribed in a semicircle has a unique 10. Use any method of your choice
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property. Engage in Activity 5.8 to to share the findings with other
study the nature of the angle formed in students for further discussion.
a semicircle.
In Activity 5.8, you might have deduced
that the angle inscribed in a semicircle
Activity 5.8: Deducing the nature measures 90° . This angle is formed at a
of the angle formed in a semicircle point on the circumference of a circle
by two chords originating from the end
points of the diameter.
Individually or in a group, perform the
following tasks:
Theorem 5.5
1. Trace a circle of convenient radius The angle subtended at the
on the geoboard.
circumference by the diameter
2. Trace an angle on the circumference of a circle is a right angle. This
of the circle formed by two is referred to as “angle in a
intersecting line segments passing semicircle”.
through the end points of the
diameter. Theorem 5.5 is described geometrically
3. Measure the angle traced in task 2. as follows.
̂
4. Repeat tasks 2 and 3 several times, In Figure 5.16, A C B is formed on the
circumference of a semicircle by two
Mathematics for Secondary Schools 5. Record all the angles measured and Theorem 5.5, it implies that ACB 90 .= °.
each time changing the position of
chords AC and BC originating from
the point of intersection of the two
each end point of the diameter. Using
lines.
ˆ
C
note down any unique result.
6. Draw similar figures in your
exercise book and measure the
angles.

7. What have you generally noticed on
the nature of all the angles formed?
8. Write a general rule regarding the A O B
nature of the angle formed in a
semicircle. Figure 5.16: Angle in a semicircle

136 Student\s Book Form Three

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