Theorems on Angles and Arcs

The video tutorial covers theorems related to central angles, arcs, and chords in geometry. It explains three main theorems: the relationship between central angles and their arcs, the connection between central angles and chords, and the link between arcs and chords. The tutorial includes problem-solving examples to apply these theorems, demonstrating how congruent angles lead to congruent arcs and chords, and how the circle's properties are used to find unknown values.

What is the main focus of the video tutorial?

• Theorems on central angles, arcs, and chords

• Theorems on triangles and quadrilaterals

• Theorems on parallel lines and transversals

• Theorems on polygons and their properties

How many main theorems are discussed in the video?

• Four

• Two

• Three

• Five

According to the first theorem, if two central angles are congruent, what can be said about their corresponding arcs?

• The arcs are not related

• The arcs are parallel

• The arcs are perpendicular

• The arcs are congruent

In the first theorem, if angle BAC is congruent to angle EAD, what can be said about arc BC and arc ED?

• Arc BC is larger than arc ED

• Arc BC is perpendicular to arc ED

• Arc BC is smaller than arc ED

• Arc BC is congruent to arc ED

According to the second theorem, if two central angles are congruent, what can be said about their corresponding chords?

• The chords are parallel

• The chords are perpendicular

• The chords are congruent

• The chords are not related

In the second theorem, if angle BAC is congruent to angle EAD, what can be said about chord BC and chord ED?

• Chord BC is longer than chord ED

• Chord BC is perpendicular to chord ED

• Chord BC is shorter than chord ED

• Chord BC is congruent to chord ED

According to the third theorem, if two chords are congruent, what can be said about their corresponding arcs?

• The arcs are not related

• The arcs are congruent

• The arcs are perpendicular

• The arcs are parallel

In the third theorem, if chord BC is congruent to chord ED, what can be said about arc BC and arc ED?

• Arc BC is congruent to arc ED

• Arc BC is larger than arc ED

• Arc BC is smaller than arc ED

• Arc BC is perpendicular to arc ED

If angle BAC is 65 degrees, what is the measure of arc BC according to the first theorem?

• 90 degrees

• 65 degrees

• 180 degrees

• 30 degrees

If angle EAD is 30 degrees, what is the measure of arc ED according to the first theorem?

• 30 degrees

• 65 degrees

• 90 degrees

• 180 degrees