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Learn about common tangents, identifying tangents, missing values, tangents in polygons, and real-world applications. Practice with examples and 5-minute checks to enhance understanding.

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 10–4) CCSS 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

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

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

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

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

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

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

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

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

  11. find x if mA = 3x + 9 and mB = 8x – 4. A. 10 B. 11 C. 12 D. 13 5-Minute Check 5

  12. find x if mA = 3x + 9 and mB = 8x – 4. A. 10 B. 11 C. 12 D. 13 5-Minute Check 5

  13. 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

  14. 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

  15. Content Standards G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). G.C.4 Construct a tangent line from a point outside a given circle to the circle. Mathematical Practices 1 Make sense of problems and persevere in solving them. 2 Reason abstractly and quantitatively. CCSS

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

  17. tangent • point of tangency • common tangent Vocabulary

  18. Identify Common Tangents A. Copy the figure and draw the common tangents. If no common tangent exists, state no common tangent. Answer: Example 1

  19. 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

  20. Identify Common Tangents B. Copy the figure and draw the common tangents. If no common tangent exists, state no common tangent. Answer: Example 1

  21. 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

  22. 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

  23. 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

  24. 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

  25. 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

  26. Concept

  27. ? 202 + 212 = 292 Pythagorean Theorem Identify a Tangent Test to see if ΔKLM is a right triangle. 841 = 841 Simplify. Answer: Example 2

  28. ? 202 + 212 = 292 Pythagorean Theorem Answer: Identify a Tangent Test to see if ΔKLM is a right triangle. 841 = 841 Simplify. Example 2

  29. A. B. Example 2

  30. A. B. Example 2

  31. Use a Tangent to Find Missing Values EW2 + DW2 = DE2 Pythagorean Theorem 242 + x2 = (x + 16)2EW = 24, DW = x, and DE = x + 16 576 + x2 = x2 + 32x + 256 Multiply. 320 = 32x Simplify. 10 = x Divide each side by 32. Answer: Example 3

  32. Use a Tangent to Find Missing Values EW2 + DW2 = DE2 Pythagorean Theorem 242 + x2 = (x + 16)2EW = 24, DW = x, and DE = x + 16 576 + x2 = x2 + 32x + 256 Multiply. 320 = 32x Simplify. 10 = x Divide each side by 32. Answer: x = 10 Example 3

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

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

  35. Concept

  36. 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: Example 4

  37. 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

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

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

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

  41. Find Measures in Circumscribed Polygons Step 2 Find the perimeter of ΔQRS. = 10 + 2 + 8 + 6 + 10 or 36 cm Answer: Example 5

  42. 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

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

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

  45. End of the Lesson

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