Perform the activity above at least three times, and record your observations on ½ crosswise paper using this table format.
10- OBUSAN Arc and Angle Measure in Circle
[b][color=#0000ff][size=150]In this activity you will discover relationships in circles that involve arc and angle measures.[/size][/color][/b]
Part I. Angles Formed in the interior of a Circle by Two Intersecting Chords/Secants
Chords are segments that have both endpoints on a circle. Secants are lines that contain a chord. When two chords/secants intersect inside of a circle, four angles are formed. At the point of intersection, two sets of congruent vertical angles are formed. [br]
Refer to the Circle below.
Give one pair of vertical angles formed by two intersecting chords and name their intercepted arcs.
Engage with the applet below and move points [b]D[/b],[b]C[/b],[b]B[/b], and [b]E[/b] to discover the relationship between the measure of the angles formed by intersecting chords and the measures of their intercepted arcs.
Record your observations in your paper.
What is the relationship between the measures of angles formed by chords and the measures of their intercepted arcs?
If the intercepted arcs are 32 degrees and 54 degrees, what is the angle measure of the vertical angles?
Part II. Angles Formed in the exterior of a Circle by two intersecting secants/tangents
A secant line intersects a circle at two points, while a tangent line intersects the circle at only one point. When two lines intersect outside the circle, they intercept two arcs .
Refer to the Circle below.
Name the angle formed by two intersecting secants and name its intercepted arcs.
Use the applet below and move points[b] D,C,B[/b], and[b] E [/b]to discover the relationship between the measure of the angle created by two secant lines and the measure of the intercepted arcs.
Record your Observation using this format.
Perform the activity above at least three times, and record your observations on ½ crosswise paper using this table format.
What is the relationship between the measure of the angle formed by two secant lines and the measures of the intercepted arcs?
If the intercepted arcs by the two secants measure 190 degrees and 30 degrees , what is the measure of the angle formed?
Exit Ticket!
What is one thing you learned today?