Using Inscribed Angles & Polygons; Justifying
Measurements & Relationships in Circles
14-1Inscribed Angles
Using Inscribed Angles & Polygons; Justifying
Measurements & Relationships in Circles
Inscribed Angle:
An angle whose
vert...
Using Inscribed Angles & Polygons; Justifying
Measurements & Relationships in Circles
Name the intercepted arc for the
ang...
Using Inscribed Angles & Polygons; Justifying
Measurements & Relationships in Circles
Name the intercepted arc for the
ang...
Using Inscribed Angles & Polygons; Justifying
Measurements & Relationships in Circles
2
ArcdIntercepte
AngleInscribed =
16...
Using Inscribed Angles & Polygons; Justifying
Measurements & Relationships in Circles
120
x
What do we call this type of a...
120
x
What is the value of x?
y
How do we solve for y?
The measure of the inscribed angle is HALF the
measure of the inscr...
Using Inscribed Angles & Polygons; Justifying
Measurements & Relationships in Circles
Examples
3. If m JK = 80°, find m ∠J...
Using Inscribed Angles & Polygons; Justifying
Measurements & Relationships in Circles
72º
If two inscribed angles intercep...
Using Inscribed Angles & Polygons; Justifying
Measurements & Relationships in Circles
Example 5
In J, m∠3 = 5x and m∠ 4 =...
Using Inscribed Angles & Polygons; Justifying
Measurements & Relationships in Circles
Example 5
In J, m∠3 = 5x and m∠ 4 =...
Using Inscribed Angles & Polygons; Justifying
Measurements & Relationships in Circles
Example 5
In J, m∠3 = 5x and m∠ 4 =...
Using Inscribed Angles & Polygons; Justifying
Measurements & Relationships in Circles
180º
d
ia
m
eter
If a right
triangle...
Using Inscribed Angles & Polygons; Justifying
Measurements & Relationships in Circles
•
H
K
G
N
4x – 14 = 90
Example 6
GH ...
Using Inscribed Angles & Polygons; Justifying
Measurements & Relationships in Circles
•
H
K
G
N
6x – 5 + 3x – 4 = 90
Examp...
Upcoming SlideShare
Loading in …5
×

14 1 inscribed angles and intercepted arcs

3,443 views

Published on

Published in: Technology, Business
0 Comments
1 Like
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total views
3,443
On SlideShare
0
From Embeds
0
Number of Embeds
975
Actions
Shares
0
Downloads
95
Comments
0
Likes
1
Embeds 0
No embeds

No notes for slide

14 1 inscribed angles and intercepted arcs

  1. 1. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles 14-1Inscribed Angles
  2. 2. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles Inscribed Angle: An angle whose vertex is on the circle. INSCRIBED ANGLE INTERCEPTED ARC
  3. 3. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles Name the intercepted arc for the angle. • C L O T 1. CL
  4. 4. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles Name the intercepted arc for the angle. • Q R K V 2. QVR S • • • •
  5. 5. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles 2 ArcdIntercepte AngleInscribed = 160º 80º To find the measure of an inscribed angle…
  6. 6. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles 120 x What do we call this type of angle? What is the value of x? y How do we solve for y? The measure of the inscribed angle is HALF the measure of the inscribed arc!!
  7. 7. 120 x What is the value of x? y How do we solve for y? The measure of the inscribed angle is HALF the measure of the inscribed arc!! Since we know that the measure of x AND the measure of y must both equal half of 120, then we know that x=y 120/2 = 60 X= 60 Y= 60
  8. 8. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles Examples 3. If m JK = 80°, find m ∠JMK. • M Q K S J 4. If m ∠MKS = 56°, find m MS. 40 ° 112 °
  9. 9. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles 72º If two inscribed angles intercept the same arc, then they are congruent. Therefore we can say that the blue angle and the red angle have the same angle measurement
  10. 10. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles Example 5 In J, m∠3 = 5x and m∠ 4 = 2x + 9. Find the value of x. 3 • Q D JT U 4Find m∠ 4 Find arc QD Find arc QTD
  11. 11. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles Example 5 In J, m∠3 = 5x and m∠ 4 = 2x + 9. Find the value of x. 3 • Q D JT U 4 Since we know that angle 3 and 4 intersect the same arc, we know that they must be congruent, so we can set them equal to one another to find x. TRY IT!
  12. 12. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles Example 5 In J, m∠3 = 5x and m∠ 4 = 2x + 9. Find the value of x. 3 • Q D JT U 4
  13. 13. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles 180º d ia m eter If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle.
  14. 14. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles • H K G N 4x – 14 = 90 Example 6 GH is a diameter and m∠GNH = 4x – 14. Find the value of x. x = 26
  15. 15. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles • H K G N 6x – 5 + 3x – 4 = 90 Example 7 In K, m∠1 = 6x – 5 and m∠2 = 3x – 4. Find the value of x. x = 11 1 2

×