Embed Size (px)
DESCRIPTION
Transparency 10-4. 5-Minute Check on Lesson 10-3. The radius of ⊙ R is 35, LM NO , LM = 45 and m LM = 80. Find each measure . m NO m NQ NO NT RT Which congruence statement is true if RS and TU are congruent chords of ⊙ V ?. 80 °. 40 °. - PowerPoint PPT Presentation
Citation preview
5-Minute Check on Lesson 10-35-Minute Check on Lesson 10-35-Minute Check on Lesson 10-35-Minute Check on Lesson 10-3 Transparency 10-4
Click the mouse button or press the Click the mouse button or press the Space Bar to display the answers.Space Bar to display the answers.
The radius of ⊙R is 35, LM NO, LM = 45 and mLM = 80.Find each measure.
1. m NO
2. m NQ
3. NO
4. NT
5. RT
6. Which congruence statement is true if RS and TU are congruent chords of ⊙V?Standardized Test Practice:
A CB DRS SU RS TU ST RU RS ST
45
80°
40°
22.5
26.81
B
Lesson 10-4
Inscribed Angles
Objectives
• Find measures of inscribed angles
• Find measures of angles of inscribed polygons
Vocabulary
• Inscribed Angle – an angle with its vertex on the circle and chords as its sides
Circles – Inscribed Anglesy
x
F
E
J
K
Inscribe A
ngles
-- M
easure Y
° = ½
X°
(central a
ngle)
Center
X°
Y°
Measure Y° = ½ measure Arc KEF
In and Find the measures of the numbered angles.
First determine
Arc Addition Theorem
Simplify.
Subtract 168 from each side.
Divide each side by 2.
So, m
Answer:
In and Find the measures of the numbered angles.
Answer:
ALGEBRA Triangles TVU and TSU are inscribed in with Find the measure of each numbered angle if and
∆UVT and ∆ UST are right triangles. Since they intercept congruent arcs, then m1 = m2. The third angles of the triangles must also be congruent, so m2 = m4 .
Angle Sum Theorem
Simplify.
Subtract 105 from each side.
Divide each side by 3.Use the value of x to find the measures of
Given
Given
Answer:
Answer:
ALGEBRA Triangles MNO and MPO are inscribed in with Find the measure of each numbered angle if and
Quadrilateral QRST is inscribed in If and Find and
Draw a sketch of this situation.
To find we need to know
To find first find
Inscribed Angle Theorem
Sum of angles in circle = 360
Subtract 174 from each side.
Inscribed Angle Theorem
Substitution
Divide each side by 2.
To find we need to know but first we must find
Inscribed Angle Theorem
Sum of angles in circle = 360
Subtract 204 from each side.
Inscribed Angle Theorem
Divide each side by 2.
Answer:
Answer:
Quadrilateral BCDE is inscribed in If and find and
Summary & Homework
• Summary:– The measure of the inscribed angle is half the
measure of its intercepted arc– The angles of inscribed polygons can be found by
using arc measures
• Homework: – pg 549-550; 7, 9,10, 15, 22-25
