grade 10 math for theorems in english

2. LESSON OBJECTIVES:
❖ Illustrate congruent circles and
congruent arcs.
❖ Define and illustrate theorems
on chords, arcs, central angles,
and inscribed angles.

3. CONGRUENT CIRCLES
Circles with congruent radii are said to be
congruent.

4. CONGRUENT ARCS
Arcs of the same circle or congruent circles
which have equal measures are said to be
congruent.

5. PART 1:
Theorems on Central Angles,
Arcs, and Chords

9. Consider the figure below.
•

10. Consider the figure below.
•

11. Consider the figure below.
•

13. PART 2:
Theorems on Inscribed Angles

14. INSCRIBED ANGLES AND
INTERCEPTED ARCS
An inscribed angle is an angle formed whose
vertex is on the circle and whose sides
contain the chords of the circle.
An intercepted arc lies in the inner portion of
an inscribed angle and whose endpoints is
on the angle.

16. INSCRIBED ANGLE THEOREM
In a circle, if an angle is inscribed in it, then half the
measure of the intercepted arc is the measure of the
inscribed angle (or twice the measure of the inscribed
angle is equal to the measure of the intercepted arc).

17. CONGRUENT INSCRIBED ANGLES
In a circle, the inscribed angles subtended
by the same arc are congruent.

18. INSCRIBED ANGLE IN A SEMICIRCLE
In a circle, if an angle is inscribed in it intercepts a
semicircle, then the angle formed is a right angle.

19. CYCLIC QUADRILATERAL IN A CIRCLE
Cyclic quadrilateral is the term which refers to an inscribed
quadrilateral in a circle. The opposite angles of a cyclic
quadrilateral are supplementary. Supplementary angles are
pairs of angles whose sum is 180°.

20. WHAT’S NEXT???
Illustrate sectors and
segments of a circle.