5-minute check on lesson 10-3

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