<p>Secondary 3 (Grade 9) Geometry</p><p>Guiding Question Angles, Angles in the Circle, What Do You Know About Them?</p><p>Topic Angle Properties of Circles</p><p>Software Required Cabri-Jr. Application for the TI-83 Plus Graphics Calculator</p><p>Level Secondary 3 (Grade 9)</p><p>Duration Three 40-minute periods</p><p>Objective To investigate the following angle properties of circles: 1. Angles in the same segment are equal. 2. Angle at the center is twice angle at the circumference. 3. Opposite angles of a cyclic quadrilateral are supplementary.</p><p>Pre-requisite Knowledge Students have been introduced to the following terms in Geometry: 1. Arc – major and minor 2. Chord and diameter 3. Segment – major and minor 4. Sector – major and minor 5. Angle at the center 6. Angle at the circumference 7. Cyclic quadrilateral</p><p>Construction Property 2: 1. Draw a circle. 2. Construct a segment from the center of the circle, O, to a point on the circumference (A). 3. Construct another segment from the center of the circle to another point on the circumference (B). 4. Construct two segments to join A and B to a new point on the circumference (C). 5. Measure the angle ACB. 6. Measure also the angle AOB. 7. Observe the relationship between the two angles. 8. Animate point A or point B.</p><p>NIE2004/Inquiry Learning/TCHS/Sec3(Grade9)/Mok SL 9. Stop the animation at different points on the circumference. 10. Observe the relationship between the two angles at the different points. 11. Discussion: What conjecture can you make about the relationship between the two angles?</p><p>Property 1: 1. How can you use the construction in Property 2 to prove Property 1? 2. Discussion: In groups of two or three, use the software to make the connection.</p><p>Property 3: 1. Draw a circle. 2. Draw a quadrilateral within the circle with its vertices on the circumference of the circle drawn earlier. 3. Measure two opposite angles within the quadrilateral. 4. Animate the vertex of either one of the two angles. 5. Note the values of the measurements of the two opposite angles as the animation progresses. 6. Discussion: What conjecture can you make about the relationship of the two opposite angles? As you animate the vertex of one of the two angles, why does the value of the angle toggle between two values only? Hint: Use the properties earlier to explain.</p><p>NIE2004/Inquiry Learning/TCHS/Sec3(Grade9)/Mok SL</p>