Unit 14 - Circles - Proofs

Question 1

Proofs for Central Angles (2)

Answer 1

1. In a circle, measure of CA ≅ measure of intercepted arc
2. In a circle, ≅ central angles have ≅ arcs

Question 3

Proofs for Semicircles (2)

Answer 3

1. In a circle, an angle inscribed in a semicircle is right
2. A triangle inscribed in a semicircle is right

Question 4

Proof for Inscribed Angles

Answer 4

In a circle, inscribed ∠ that intercept same/≅ arcs are ≅

Question 5

Proof for Congruent Circles

Answer 5

Two circles with ≅ radii are ≅

Question 6

Proof for Chords & Arcs (5)

Answer 6

1. In a circle, ≅ chords have ≅ arcs
2. In a circle, ≅ arcs have ≅ chords
3. In a circle, ≅ central angles have ≅ chords
4. In a circle, ≅ chords have ≅ central angles
5. In a circle, parallel lines intercept ≅ arcs

Question 7

Proofs for Bisecting Chords/Arcs (2)

Answer 7

1. If diameter of circle ⊥ to chord, meets chord/arc at mp
2. A midpt of a segment/arc divides to 2 ≅ segment/arc

Question 8

Proofs for Tangents (2)

Answer 8

1. Two tangents drawn to a circle from same external point are ≅ in length
2. Tangent drawn to a radius is ⊥ to radius drawn to the point of tangency