Five-Minute Check (over Lesson 10–4)NGSSSThen/NowNew VocabularyExample 1:Identify Common TangentsTheorem 10.10Example 2:Identify a TangentExample 3:Use a Tangent to Find Missing ValuesTheorem 10.11Example 4:Use Congruent Tangents to Find MeasuresExample 5:Real-World Example: Find Measures in Circimscribed

Polygons

Over Lesson 10–4

A. AB. BC. CD. D

A B C D

0% 0%0%0%

A. 60

B. 55

C. 50

D. 45

Refer to the figure. Find m1.

Over Lesson 10–4

A. AB. BC. CD. D

A B C D

0% 0%0%0%

A. 30

B. 25

C. 20

D. 15

Refer to the figure. Find m2.

Over Lesson 10–4

A. AB. BC. CD. D

A B C D

0% 0%0%0%

A. 35

B. 30

C. 25

D. 20

Refer to the figure. Find m3.

Over Lesson 10–4

A. AB. BC. CD. D

A B C D

0% 0%0%0%

A. 120

B. 100

C. 80

D. 60

Refer to the figure. Find m4.

Over Lesson 10–4

A. AB. BC. CD. D

A B C D

0% 0%0%0%

A. 10

B. 11

C. 12

D. 13

find x if mA = 3x + 9 and mB = 8x – 4.

Over Lesson 10–4

A. AB. BC. CD. D

A B C D

0% 0%0%0%

A. 47.5°

B. 95°

C. 190°

D. 265°

The measure of an arc is 95°. What is the measure of an inscribed angle that intercepts it?

MA.912.G.6.1 Determine the center of a given circle. Given three points not on a line, construct the circle that passes through them. Construct tangents to circles. Circumscribe and inscribe circles about and within triangles and regular polygons. MA.912.G.6.4 Determine and use measures of arcs and related angles. Also addresses MA.912.G.6.2 and MA.912.G.6.3.

You used the Pythagorean Theorem to find side lengths of right triangles. (Lesson 8–2)

• Use properties of tangents.• Solve problems involving circumscribed

polygons.

• tangent• point of tangency• common tangent

Identify Common Tangents

A. Copy the figure and draw the common tangents. If no common tangent exists, state no common tangent.

Answer: These circles have no common tangents. Any tangent of the inner circle will intercept the outer circle in two points.

Identify Common Tangents

B. Copy the figure and draw the common tangents. If no common tangent exists, state no common tangent.

Answer: These circles have 2 common tangents.

A. AB. BC. CD. D

A B C D

0% 0%0%0%

A. 2 common tangents

B. 4 common tangents

C. 6 common tangents

D. no common tangents

A. Copy the figure and draw the common tangents to determine how many there are. If no common tangent exists, choose no common tangent.

A. AB. BC. CD. D A B C D

0% 0%0%0%

A. 2 common tangents

B. 3 common tangents

C. 4 common tangents

D. no common tangents

B. Copy the figure and draw the common tangents to determine how many there are. If no common tangent exists, choose no common tangent.

Identify a Tangent

Test to see if ΔKLM is a right triangle.?202 + 212 = 292 Pythagorean Theorem

841 = 841 Simplify.

Answer:

A. AB. B

A B

0%0%

A.

B.

Use a Tangent to Find Missing Values

EW 2 + DW

2 = DE 2 Pythagorean Theorem

242 + x 2 = (x + 16)2 EW = 24, DW = x, and

DE = x + 16576 + x

2 = x 2 + 32x + 256 Multiply.

320 = 32x Simplify.10 = x Divide each side by 32.

Answer: x = 10

A. AB. BC. CD. D

A B C D

0% 0%0%0%

A. 6

B. 8

C. 10

D. 12

Use Congruent Tangents to Find Measures

AC = BC Tangents from the same exteriorpoint are congruent.

3x + 2 = 4x – 3 Substitution2 = x – 3 Subtract 3x from each side.5 = x Add 3 to each side.

Answer: x = 5

A. AB. BC. CD. D

A B C D

0% 0%0%0%

A. 5

B. 6

C. 7

D. 8

Find Measures in Circumscribed Polygons

Step 1 Find the missing measures.

Find Measures in Circumscribed Polygons

Step 2 Find the perimeter of ΔQRS.

Answer: So, the perimeter of ΔQRS is 36 cm.

= 10 + 2 + 8 + 6 + 10 or 36 cm

A. AB. BC. CD. D

A B C D

0% 0%0%0%

A. 42 cm

B. 44 cm

C. 48 cm

D. 56 cm