Identify special segments and lines

1
Identify special segments and lines
Example 1
Solution
radius
secant
tangent
2
Find lengths in circles in a coordinate plane
Example 2
Use the diagram to find the given lengths.
Solution
2
4
4
8
3
Checkpoint. Complete the following exercises.

1. In Example 1, tell whether AB is best described
   as a radius, chord, diameter, secant, or tangent.
   Explain.

4
Checkpoint. Complete the following exercises.
5
Draw common tangents
Example 3
Tell how many common tangents the circles have
and draw them.
Solution
2
3
1

1. ___ common tangents

1. ___ common tangents

1. ___ common tangents

6
Checkpoint. Tell how many common tangents the
circles have and draw them.
no common tangents
4 common tangents
7
Theorem 6.1
If a plane, a line is tangent to a circle if and
only if the line is _____________ to the radius
of the circle at its endpoint on the circle.
perpendicular
P
8
Verify a tangent to a circle
Example 4
Solution
right triangle
Theorem 6.1
tangent
9
(No Transcript)
10
NO
11
Find the radius of a circle
Example 5
Solution
right triangle
Pythagorean Theorem
Substitute.
Multiply.
Subtract from each side.
98
Divide by ____.
36
12
Checkpoint. Complete the following exercises.

1. In the diagram, K is a point of tangency. Find
   the radius r of L.

13
Theorem 6.2
Tangent segments from a common external point are
_____________.
congruent
14
Use properties of tangents
Example 6
Solution
Tangent segments from a common external point are
___________.
congruent
Substitute.
Solve for x.
15
Triangle Similarity Postulates and Theorems
Angle-Angle (AA) Similarity Postulate
congruent
If two angles of one triangle are ___________ to
two angles of another _________, then the two
triangles are _________.
triangle
similar
Theorem 6.3 Side-Side-Side (SSS) Similarity
Theorem
If the corresponding side lengths of two
triangles are _____________, then the triangles
are _________.
proportional
similar
Theorem 6.4 Side-Angle-Side (SAS) Similarity
Theorem
congruent
If an angle of one triangle is _____________ to
an angle of a second triangle and the lengths of
the sides including these angles are
______________, then the triangles are ________.
similar
proportional
16
Use tangents with similar triangles
Example 7
Solution
Theorem 6.1
______________
Reflexive Prop
______________
AA Similarity Post
Corr. sides lengths are prop.
17
Checkpoint. Complete the following exercises.
18
Pg. 198, 6.1 1-34