Geometry Chapter 10 Theorems and Postulates

Question 1

t-10.1

Answer 1

a line can only be tangent if the line is perpendicular to be he radius

Question 2

t-10.2

Answer 2

tangent segments from a common external point are congruent

Question 3

arc addition postulate

Answer 3

if arc ABC, then arc AB plus arc AC equals arc ABC

Question 4

t-10.3

Answer 4

in the same or two congruent circles, minor arc sides have to be congruent for the arcs to be congruent

Question 5

t-10.4

Answer 5

if one chord is a perpendicular bisect or of another chord, then the first chord is a diameter

Question 6

t-10.5

Answer 6

if a diameter of a circle is perpendicular to a chord, then it will bisect that chord and it’s arc

Question 7

t-10.6

Answer 7

in the same circle, or in congruent circles, two chords are congruent if and only if they they are equidistant from the center

Question 8

t-10.7

Answer 8

the measure of an inscribed angle is half the measure of its intercepted arc

Question 9

t-10.8

Answer 9

if two inscribed angles intercept the same arc, then the angles are congruent

Question 10

t-10.9

Answer 10

if a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. Conversely, if one side of an inscribed triangle is a diameter of the circle, then the triangle is a right triangle and the opposite angle is the right angle

Question 11

t-10.10

Answer 11

a quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary