LESSON 10 5 Tangents FiveMinute Check over Lesson

Five-Minute Check (over Lesson 10– 4) TEKS Then/Now New Vocabulary Example 1: Identify Common

Over Lesson 10– 4 Refer to the figure. Find m 1. A. 60 B.

Over Lesson 10– 4 Refer to the figure. Find m 2. A. 30 B.

Over Lesson 10– 4 Refer to the figure. Find m 3. A. 35 B.

Over Lesson 10– 4 Refer to the figure. Find m 4. A. 120 B.

Over Lesson 10– 4 find x if m A = 3 x + 9

Over Lesson 10– 4 The measure of an arc is 95°. What is the

Targeted TEKS G. 12(A) Apply theorems about circles, including relationships among angles, radii, chords,

You used the Pythagorean Theorem to find side lengths of right triangles. • Use

• tangent • point of tangency • common tangent

Identify Common Tangents A. Copy the figure and draw the common tangents. If no

Identify Common Tangents B. Copy the figure and draw the common tangents. If no

A. Copy the figure and draw the common tangents to determine how many there

B. Copy the figure and draw the common tangents to determine how many there

Identify a Tangent Test to see if ΔKLM is a right triangle. 2 2

Use a Tangent to Find Missing Values EW 2 + DW 2 = DE

Use Congruent Tangents to Find Measures AC = BC 3 x + 2 =

Find Measures in Circumscribed Polygons Step 1 Find the missing measures.

Find Measures in Circumscribed Polygons Step 2 Find the perimeter of ΔQRS. = 10

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LESSON 10– 5 Tangents

Five-Minute Check (over Lesson 10– 4) TEKS Then/Now New Vocabulary Example 1: Identify Common Tangents Theorem 10. 10 Example 2: Identify a Tangent Example 3: Use a Tangent to Find Missing Values Theorem 10. 11 Example 4: Use Congruent Tangents to Find Measures Example 5: Real-World Example: Find Measures in Circimscribed Polygons

Over Lesson 10– 4 Refer to the figure. Find m 1. A. 60 B. 55 C. 50 D. 45

Over Lesson 10– 4 Refer to the figure. Find m 2. A. 30 B. 25 C. 20 D. 15

Over Lesson 10– 4 Refer to the figure. Find m 3. A. 35 B. 30 C. 25 D. 20

Over Lesson 10– 4 Refer to the figure. Find m 4. A. 120 B. 100 C. 80 D. 60

Over Lesson 10– 4 find x if m A = 3 x + 9 and m B = 8 x – 4. A. 10 B. 11 C. 12 D. 13

Over Lesson 10– 4 The measure of an arc is 95°. What is the measure of an inscribed angle that intercepts it? A. 47. 5° B. 95° C. 190° D. 265°

Targeted TEKS G. 12(A) Apply theorems about circles, including relationships among angles, radii, chords, tangents, and secants, to solve non-contextual problems. Mathematical Processes G. 1(A), G. 1(E)

You used the Pythagorean Theorem to find side lengths of right triangles. • 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. Copy the figure and draw the common tangents to determine how many there are. If no common tangent exists, choose no common tangent. A. 2 common tangents B. 4 common tangents C. 6 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. A. 2 common tangents B. 3 common tangents C. 4 common tangents D. no common tangents

Identify a Tangent Test to see if ΔKLM is a right triangle. 2 2 ? 20 + 21 = 292 841 = 841 Answer: Pythagorean Theorem Simplify.

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 + 32 x + 256 Multiply. 320 = 32 x 10 = x Answer: x = 10 Simplify. Divide each side by 32.

A. 6 B. 8 C. 10 D. 12

Use Congruent Tangents to Find Measures AC = BC 3 x + 2 = 4 x – 3 Tangents from the same exterior point are congruent. Substitution 2= x– 3 Subtract 3 x from each side. 5= x Add 3 to each side. Answer: x = 5

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. = 10 + 2 + 8 + 6 + 10 or 36 cm Answer: So, the perimeter of ΔQRS is 36 cm.

A. 42 cm B. 44 cm C. 48 cm D. 56 cm

LESSON 10– 5 Tangents