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 Lesson Menu

Refer to the figure. Find m1. A. 60 B. 55 C. 50 D. 45 5-Minute Check 1

Refer to the figure. Find m2. A. 30 B. 25 C. 20 D. 15 5-Minute Check 2

Refer to the figure. Find m3. A. 35 B. 30 C. 25 D. 20 5-Minute Check 3

Refer to the figure. Find m4. A. 120 B. 100 C. 80 D. 60 5-Minute Check 4

find x if mA = 3x + 9 and mB = 8x – 4. C. 12 D. 13 5-Minute Check 5

The measure of an arc is 95° 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° 5-Minute Check 6

Mathematical Processes G.1(A), G.1(E) 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) TEKS

Use properties of tangents. You used the Pythagorean Theorem to find side lengths of right triangles. Use properties of tangents. Solve problems involving circumscribed polygons. Then/Now

tangent point of tangency common tangent Vocabulary

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. Example 1

Answer: These circles have 2 common tangents. 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. Example 1

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 Example 1

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 Example 1

Concept

Test to see if ΔKLM is a right triangle. Identify a Tangent Test to see if ΔKLM is a right triangle. ? 202 + 212 = 292 Pythagorean Theorem 841 = 841 Simplify. Answer: Example 2

A. B. Example 2

EW 2 + DW 2 = DE 2 Pythagorean Theorem 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 Example 3

A. 6 B. 8 C. 10 D. 12 Example 3

Concept

AC = BC Tangents from the same exterior point are congruent. Use Congruent Tangents to Find Measures AC = BC Tangents from the same exterior point 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 Example 4

A. 5 B. 6 C. 7 D. 8 Example 4

Step 1 Find the missing measures. Find Measures in Circumscribed Polygons Step 1 Find the missing measures. Example 5

Step 2 Find the perimeter of ΔQRS. 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. Example 5

A. 42 cm B. 44 cm C. 48 cm D. 56 cm Example 5

LESSON 10–5 Tangents