Question

explore: what do you notice? drag inscribed angles $\angle$l1 & $\angle$l2. what do you notice?

Explanation:

When dragging inscribed angles ∠1 and ∠2 that subtend the same arc (or congruent arcs) in a circle, we observe that the measures of these inscribed angles are equal. This is due to the Inscribed Angle Theorem, which states that an angle θ subtended by an arc at the circumference of a circle is half the central angle subtended by the same arc. When two inscribed angles subtend the same (or congruent) arcs, their measures will be equal (since both will be half of the same central angle measure, or half of congruent central angle measures). For example, in the given diagram, both ∠1 and ∠2 have a measure of 30°, and the central angle subtending the same arc is 60° (which is twice 30°), illustrating that inscribed angles subtending the same arc are equal in measure.

Answer:

When dragging inscribed angles ∠1 and ∠2 (that subtend the same or congruent arcs), their measures remain equal (e.g., both are 30° here), showing that inscribed angles subtending the same arc (or congruent arcs) in a circle have equal measures (by the Inscribed Angle Theorem).