1. Friday-Chapter 6 Quiz 2 on 6.1-6.3
Lesson 6.3 Inscribed Angles and their Intercepted Arcs
Objectives:
Using Inscribed Angles
Using Properties of Inscribed Angles.
Homework: Lesson 6.3/ 1-12
Friday-Chapter 6 Quiz 2 on

2. Inscribed Angles & Intercepted Arcs
Using Inscribed Angles
Inscribed Angles & Intercepted Arcs
An INSCRIBED ANGLE is an angle whose vertex is on the circle and whose sides are chords of a circle.
∠ABC is an inscribed angle

3. Measure of an Inscribed Angle
Using Inscribed Angles
Measure of an Inscribed Angle

4. Find the m and mPAQ . = 2 * m PBQ = 2 * 63 = 126˚ Example 1: 63°
Using Inscribed Angles
Example 1:
Find the m and mPAQ .
= 2 * m PBQ
= 2 * 63
= 126˚
63°

5. Q R Find the measure of each arc or angle. = ½ 120 = 60˚ = 180˚
Using Inscribed Angles
Example 2:
Find the measure of each arc or angle. Q
= ½ 120 = 60˚
= 180˚ R
= ½(180 – 120)
= ½ 60
= 30˚

6. Inscribed Angles Intercepting Arcs Conjecture
Using Inscribed Angles
Inscribed Angles Intercepting Arcs Conjecture
If two inscribed angles intercept the same arc or arcs of equal measure then the inscribed angles have equal measure.
mCAB = mCDB

7. Using Inscribed Angles
Example 3:
Find
=360 – 140 = 220˚

8. Find mCAB and m mCAB = ½ mCAB = 30˚ m = 2* 41˚ m = 82˚ Example 4:
Using Properties of Inscribed Angles
Example 4:
Find mCAB and m
mCAB = ½
mCAB = 30˚
m = 2* 41˚
m = 82˚

9. Cyclic Quadrilateral Quadrilateral ABFE is inscribed in Circle O.
Using Properties of Inscribed Angles
Cyclic Quadrilateral
A polygon whose vertices lie on the circle, i.e. a quadrilateral inscribed in a circle.
Quadrilateral ABFE is inscribed in Circle O.

10. Cyclic Quadrilateral Conjecture
Using Properties of Inscribed Angles
Cyclic Quadrilateral Conjecture
If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.
m∠A + m∠C = 180°
m∠B + m∠D = 180°

11. Find the measure of Example 5: Using Properties of Inscribed Angles
Opposite angles of an inscribed quadrilateral are supplementary
Find the measure of
Intercepted arc of an inscribed angles = 2* angle measure

12. Find m∠A and m∠B Example 6: m∠A + 60° = 180° m∠A = 120°
Opposite angles of an inscribed quadrilateral are supplementary
m∠A + 60° = 180°
m∠A = 120°
m∠B + 140° = 180°
m∠B = 40°

13. Find x and y Using Properties of Inscribed Angles Example 7:
Opposite angles of an inscribed quadrilateral are supplementary

14. Circumscribed Polygon
Using Properties of Inscribed Angles
Circumscribed Polygon
A polygon is circumscribed about a circle if and only if each side of the polygon is tangent to the circle.

15. Angles inscribed in a Semi-circle Conjecture
Using Properties of Inscribed Angles
Angles inscribed in a Semi-circle Conjecture
A triangle inscribed in a circle is a right triangle if and only if the diameter is the hypotenuse        
A has its vertex on the circle, and it intercepts half of the circle so that
mA = 90.

16. Example 8:
Angles inscribed in a semi-circle are right angles
Find x.

17. Using Inscribed Angles
Example 9:
146°
Find mFDE

18. Parallel (Secant) Lines Intercepted Arcs Conjecture
Using Properties of Inscribed Angles
Parallel (Secant) Lines Intercepted Arcs Conjecture
Parallel (secant) lines intercept congruent arcs. X A Y B

19. Using Properties of Inscribed Angles
Example 10:
Find x. x
122˚
189˚
360 – 189 – 122 = 49˚
x = 49/2 = 24.5˚ x

20. Tangent/Chord Conjecture
The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc. B B D D C C

21. Example 11:

22. Using Tangent/Chord Conjecture
Example 12:
Find x and y.
Triangle sum J
90o Q
35o yo
55o xo L K

23. Homework:
Lesson 6.3/ 1-12