Over Lesson 10–4 A.A B.B C.C D.D 5-Minute Check 1 60 Refer to the figure. Find m 1.

Transcript of Over Lesson 10–4 A.A B.B C.C D.D 5-Minute Check 1 60 Refer to the figure. Find m 1.

Over Lesson 10–4

A. A

B. B

C. C

D. D

60

Refer to the figure. Find m1.

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Over Lesson 10–4

A. A

B. B

C. C

D. D

20

Over Lesson 10–4

A. A

B. B

C. C

D. D

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Over Lesson 10–4

A. A

B. B

C. C

D. D

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

• Use properties of tangents.

• Solve problems involving circumscribed polygons.

In this lesson we will:

• tangent

• point of tangency

• common tangent

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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. A

B. B

C. C

D. D

4 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. A

B. B

C. C

D. D

3 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. A

B. B

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 + 16

576 + x 2 = x

2 + 32x + 256 Multiply.

320 = 32x Simplify.

10 = x Divide each side by 32.

Answer: x = 10

A. A

B. B

C. C

D. D

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Use Congruent Tangents to Find Measures

AC = BC Tangents from the same exteriorpoint are congruent.

3x + 2 = 4x – 3 Substitution

2 = x – 3 Subtract 3x from each side.

5 = x Add 3 to each side.

Answer: x = 5

A. A

B. B

C. C

D. D

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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. A

B. B

C. C

D. D

56 cm

Over Lesson 10–4 A.A B.B C.C D.D 5-Minute Check 1 60 Refer to the figure. Find m 1.

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