Post on 03-Jan-2016
1. Refer to the figure. The radius of is 35, = 80, LM = 45, and
LM NO. Find .
2. Find .
3. Find the measure of NO.
4. Find the measure of NT.
5. Find the measure of RT.
• intercepted
• Find measures of inscribed angles.
• Find measures of angles of inscribed polygons.
Measures of Inscribed Angles
Arc Addition Postulate
Simplify.
Subtract 168 from each side.
First determine
Divide each side by 2.
Proof with Inscribed Angles
Proof:Statements Reasons
1. Given1.
2. 2. If 2 chords are , corr. minor arcs are .
4. 4. Inscribed angles of arcs are .
5. 5. Right angles are congruent.
6. ΔPJK ΔEHG 6. AAS
3. 3. Definition of intercepted arc
Choose the best reason to complete the following proof.Given:
Prove: ΔCEM ΔHJM
1. Given
2. ______
3. Vertical angles are congruent.
4. Radii of a circle are congruent.
5. ASA
Proof:Statements Reasons
1.
2.
3.
4.
5. ΔCEM ΔHJM
1. A
2. B
3. C
4. D
A. Alternate Interior Angle Theorem
B. Substitution
C. Definition of angles
D. Inscribed angles of arcs are .
Inscribed Arcs and Probability
The probability that is the same as the probability of L being contained in .
Angles of an Inscribed Triangle
ΔUVT and ΔUVT are right triangles. m1 = m2 since they intercept congruent arcs. Then the third angles of the triangles are also congruent, so m3 = m4.
Angle Sum Theorem
Simplify.
Subtract 105 from each side.
Divide each side by 3.
Angles of an Inscribed Triangle
Use the value of x to find the measures of
Given Given
Answer:
Draw a sketch of this situation.
Angles of an Inscribed Quadrilateral
Angles of an Inscribed Quadrilateral
To find we need to know
To find first find
Inscribed Angle Theorem
Sum of arcs in circle = 360
Subtract 174 from each side.
Angles of an Inscribed Quadrilateral
Inscribed Angle Theorem
Substitution
Divide each side by 2.
Since we now know three angles of a quadrilateral, we can easily find the fourth.
mQ + mR + mS + mT = 360 360° in aquadrilateral
87 + 102 + 93 + mT = 360 Substitution
mT = 78 Subtraction
Answer: mS = 93; mT = 78