Inscribed Angles and Polygons

The video tutorial covers inscribed angles, intercepted arcs, and related theorems in geometry. It begins with an introduction to key vocabulary and concepts, followed by detailed explanations of inscribed angles and intercepted arcs. The tutorial also discusses inscribed and circumscribed polygons, providing visual examples and theorems. Special cases of inscribed angles are explored, concluding with a summary of the key points.

What is the defining characteristic of an inscribed angle?

• Its vertex is on the circle.

• It has no vertex.

• Its vertex is outside the circle.

• Its vertex is at the center of the circle.

What is an intercepted arc in relation to an inscribed angle?

• The arc that is inside the circle but not related to the angle.

• The arc that is associated with the inscribed angle.

• The arc that is outside the circle.

• The arc that is perpendicular to the inscribed angle.

What is an inscribed polygon?

• A polygon with all vertices on the circle.

• A polygon with all vertices inside the circle.

• A polygon with no vertices on the circle.

• A polygon with some vertices on the circle.

What does it mean for a circle to be circumscribed about a polygon?

• The circle is inside the polygon.

• The circle is outside the polygon.

• The circle is tangent to the polygon.

• The circle is intersecting the polygon.

According to the theorem, what is the measure of an inscribed angle?

• Three times the measure of its intercepted arc.

• Twice the measure of its intercepted arc.

• Equal to the measure of its intercepted arc.

• Half the measure of its intercepted arc.

If two inscribed angles intercept the same arc, what can be said about these angles?

• They are supplementary.

• They are unrelated.

• They are complementary.

• They are congruent.

If an inscribed angle measures 50 degrees, what is the measure of its intercepted arc?

• 25 degrees

• 50 degrees

• 100 degrees

• 200 degrees

What is the measure of an arc if the inscribed angle is 35 degrees?

• 140 degrees

• 105 degrees

• 35 degrees

• 70 degrees

If a right angle is inscribed in a circle, what is true about the hypotenuse?

• It is a diameter of the circle.

• It is a tangent to the circle.

• It is a chord of the circle.

• It is a secant of the circle.

What is the relationship between the angles if they intercept the same arc?

• They are complementary.

• They are equal.

• They are supplementary.

• They are different.