1 / 18

5-Minute Check on Lesson 10-5

Transparency 10-6. 5-Minute Check on Lesson 10-5. Determine whether each segment is tangent to the given circle . BC 2. QR Find x. Assume that the segments that appear to be tangents are tangents.

valentine-smith
Download Presentation

5-Minute Check on Lesson 10-5

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Transparency 10-6 5-Minute Check on Lesson 10-5 • Determine whether each segment is tangent to the given circle. • BC 2. QR • Find x. Assume that the segments that appear to be tangents are tangents. • 3. 4. • 5. What is the measure of PS? Yes No x = 20√5 or 44.72 x = 12 Standardized Test Practice: A B C D 18 10 B 12 14 Click the mouse button or press the Space Bar to display the answers.

  2. Lesson 10-6 Secants, Tangents, and Angle Measures

  3. Objectives • Find measures of angles formed by lines intersecting on or inside a circle • Find measures of angles formed by lines intersecting outside a circle

  4. Vocabulary • Secant – a line that intersects a circle in exactly two points

  5. y x Circles – Secants Interior Angles formed by a Secant & a Tangentm3 = ½ (m Arc JMK) m4 = ½ (m Arc JLK) M 3 K 2 4 1 J P Center Interior Angles formed by 2 Secantsm1 = ½ (m Arc MJ + m Arc LK) m2 = ½ (m Arc MK + m Arc JL) L

  6. Circles – External Angles Two Secants Secant & Tangent Two Tangents J J J K K L S T T M M M N mJ = ½(m Arc TM – m Arc TK) mJ = ½|m Arc TM – m Arc TK| mJ = ½(m Arc TMS – m Arc TS) mJ = ½|m Arc TMS – m Arc TS| mJ = ½(m Arc MN – m Arc LK) mJ = ½|m Arc MN – m Arc LK|

  7. Find if and Example 6-1a Method 1

  8. Example 6-1b Method 2 Answer: 98

  9. Find if and Example 6-1d Answer: 138

  10. Find if and Example 6-2a Answer: 55

  11. Find if and Example 6-2c Answer: 58

  12. Example 6-3a Find x. Theorem 10.14 Multiply each side by 2. Add x to each side. Subtract 124 from each side. Answer: 17

  13. Example 6-3c Find x. Answer: 111

  14. Example 6-4a JEWELRY A jeweler wants to craft a pendant with the shape shown. Use the figure to determine the measure of the arc at the bottom of the pendant. Let x represent the measure of the arc at the bottom of the pendant. Then the arc at the top of the circle will be 360 – x. The measure of the angle marked 40° is equal to 1/2 the difference of the measure of the two intercepted arcs. Multiply each side by 2 and simplify. Add 360 to each side. Divide each side by 2. Answer: 220

  15. PARKS Two sides of a fence to be built around a circular garden in a park are shown. Use the figure to determine the measure of Example 6-4c Answer: 75

  16. Example 6-5a Find x. Multiply each side by 2. Add 40 to each side. Divide each side by 6. Answer: 25

  17. Example 6-5c Find x. Answer: 9

  18. Summary & Homework • Summary: • The measure of an angle formed by two secant lines is half the positive difference of its intercepted arcs • The measure of angle formed by a secant and tangent line is half its intercepted arc • Homework: • pg 564-566; 12-14, 18-20; 23-24, 26, 29, 34-36

More Related