Unit 8 Quiz 2

Question 1

Two chords are congruent only if

Answer 1

1. Their corresponding arcs are equal so if line AB = line CD arc AB = arc CD and vice versa
2. Equidistant from the center

Question 2

If a diameter or radius is ______ to a chord then it _____ the ___ and its __

Answer 2

Perpendicular
Bisects
Chord
Arc

Question 3

Inscribed angle / arc relationship

Answer 3

The measure of the inscribed angle is = to half the measure of its intercepted arc

Ex. Inscribed angle AB measure =20
Than the arc measure = 40

Question 4

What happens when an inscribed angle intercepts a diameter

Answer 4

It is a right angle

Question 5

If two inscribed angles intercept the same arc ….

Answer 5

The angles are equal

Question 6

If a quadrilateral is inscribed in a circle then its opposite angles are ___

Answer 6

Supplementary
(Add to 180)

Question 7

A line is a tangent to a circle if and only if it is _______ to a _______ drawn to the point of tangency

Answer 7

Perpendicular
Radius

Question 8

If two segments from the same external point are tangent to a circle than they are _____

Answer 8

Congruent

Question 9

If a polygon is circumscribed around a circle then all sides are _____

Answer 9

Tangent

Question 10

Justification for chords being equal to arcs and vice versa

Answer 10

If Line AB = line CD than measure of arc AB = measure of arc CD

OR

If measure of arc AB = measure of arc CD than line AB = line CD

Question 11

Inscribed angle to arc justification

Answer 11

Angle ABC = 1/2 Arc AC

Question 12

Inscribed angles of quadrilaterals justification

Answer 12

Angle DAB + Angle BCD =180

Opp angles of inscribed quad are supplementary

Question 13

Intercepting a diameter in inscribed angles justification

Answer 13

Inscribed angles that intercept a diameter are right angles

Question 14

Overlapping arcs in inscribed angles justification

Answer 14

inscribed angles that intercept the same arc are equal

Question 15

Tangent external point justification

Answer 15

Tangent segments from same external point are equal

Question 16

Interior intersections rule

Answer 16

If two secants or chords intersect inside a circle then the measure of the angle formed is equal to half the sum of the measures of the intercepted arc
1/2 (arc AD + arc BC) for angle 1
1/2 (arc AB + arc DC) for angle 2

SEE PAGE 29

Question 17

On the circle intersections rule

Answer 17

If a secant and a tangent intersect at the point of tangency, then the measure of each angle formed is equal to half the measure of its intercepted arc
1/2 arc AB = angle 1
1/2 arc ACB = angle 2

SEE PAGE 30

Question 18

Exterior Circle intersections rules:
Two secants:
Secant and Tangent:
Two tangents:

Answer 18

1. 1/2 (arc CE - arc BD)
2. 1/2 (arc BD - arc BC)
3. 1/2 (arc BDC- arc BC)
   If secants and/or tangents intersect on the exterior of a circle, then the measure of the angle formed is equal to half the difference of the intercepted arcs

SEE PAGE 30

Question 19

Segment lengths rules

Intersecting chords/secants inside circle:
Intersecting secants outside the circle:
Intersecting secant and tangent outside the circle:

Answer 19

1. The products of one of the lines = the products of the other
   A x B = C x D
2. A (a+b) = C (c+d)
3. A squared = B (b+c)

Question 20

Special rule for two tangents hitting circle

Answer 20

If there are 2 tangents the angle formed by the 2 tangents and its nearest arc = 180