1 EXPLORATION: Lines And Line Segments That Intersect Circles
Name Dateand Segments That Intersect Circles10.1 LinesFor use with Exploration 10.1Essential Question What are the definitions of the lines and segmentsthat intersect a circle?EXPLORATION: Lines and Line Segments That Intersect CirclestenChord:ngtaWork with a partner. The drawing at the rightshows five lines or segments that intersect acircle. Use the relationships shown to write adefinition for each type of line or segment. Thenuse the Internet or some other resource to verifyyour nt:Radius:Diameter:278 GeometryStudent JournalCopyright Big Ideas Learning, LLCAll rights reserved.
Name10.12DateLines and Segments That Intersect Circles (continued)EXPLORATION: Using String to Draw a CircleWork with a partner. Use two pencils, a piece of string, and a piece of paper.a. Tie the two ends of the piece of string loosely around the two pencils.b. Anchor one pencil on the paper at the center of the circle. Use the other pencilto draw a circle around the anchor point while using slight pressure to keep thestring taut. Do not let the string wind around either pencil.c. Explain how the distance between the two pencil points as you draw the circleis related to two of the lines or line segments you defined in Exploration 1.Communicate Your Answer3. What are the definitions of the lines and segments that intersect a circle?4. Of the five types of lines and segments in Exploration 1, which one is a subset ofanother? Explain.5. Explain how to draw a circle with a diameter of 8 inches.Copyright Big Ideas Learning, LLCAll rights reserved.GeometryStudent Journal279
Name Datewith Vocabulary10.1 NotetakingFor use after Lesson 10.1In your own words, write the meaning of each vocabulary oint of tangencytangent circlesconcentric circlescommon tangentNotes:280 GeometryStudent JournalCopyright Big Ideas Learning, LLCAll rights reserved.
Name10.1DateNotetaking with Vocabulary (continued)Core ConceptsLines and Segments That Intersect CircleschordcenterA segment whose endpoints are the center and any point on a circle is aradius.radiusdiameterA chord is a segment whose endpoints are on a circle. A diameter is a chordthat contains the center of the circle.A secant is a line that intersects a circle in two points.A tangent is a line in the plane of a circle that intersects the circle in exactly one point, the point of tangency. The tangent ray AB and the tangentsegment AB are also called tangents.secantpoint oftangencytangent BNotes:ACoplanar Circles and Common TangentsIn a plane, two circles can intersect in two points, one point, or no points. Coplanarcircles that intersect in one point are called tangent circles. Coplanar circles that have acommon center are called concentric circles.2 points ofintersection1 point of intersection(tangent circles)no points ofintersectionconcentriccirclesA line or segment that is tangent to two coplanar circles is called a common tangent. Acommon internal tangent intersects the segment that joins the centers of the two circles.A common external tangent does not intersect the segment that joins the centers of thetwo circles.Notes:Copyright Big Ideas Learning, LLCAll rights reserved.GeometryStudent Journal281
Name Date10.1Notetaking with Vocabulary (continued)Extra PracticeIn Exercises 1–6, use the diagram.1. Name two radii.2. Name a chord.E3. Name a diameter.4. Name a secant.AD5. Name a tangent.6. Name a point of tangency.FBCIn Exercises 7 and 8, use the diagram.7. Tell how many common tangents the circles have and draw them.8. Tell whether each common tangent identified in Exercise 7 isinternal or external.In Exercises 9 and 10, point D is a point of tangency.9. Find BD.CA10. Point C is also a point of tangency. If BC 4 x 6, findthe value of x to the nearest tenth.105.5D282 GeometryStudent JournalBCopyright Big Ideas Learning, LLCAll rights reserved.
Coplanar Circles and Common Tangents In a plane, two circles can intersect in two points, one point, or no points. Coplanar circles that intersect in one point are called tangent circles. Coplanar circles that have a common center are called concentric circles. A line or segment that is tangent to two coplanar circles is called a common tangent. A
5 What Are Lines And Stanzas? Line A line is pretty self-explanatory. Line A line of a poem is when it jumps Line To a new, well, line, Line Like this! Line Sometimes a line is a complete sentence. Line But it doesn’t Line Have to be! Line A stanza is kind of like a paragraph. Line Stanzas are made up of lines. Line This “stanza” has five lines.
1. Lines that do not intersect are parallel lines. 2. Skew lines are coplanar. 3. Transversal is a line that intersects two or more lines. 4. Perpendicular lines are intersecting lines. 5. If two lines are parallel to a third line, then the two lines are parallel. You have just tried describing parallel and perpendicular lines. In
All vertical lines are parallel. Notes: Perpendicular Lines and Slopes Two lines in the same plane that intersect to form right angles are perpendicular lines. Nonvertical lines are perpendicular if and only if their slopes are negative reciprocals. Vertical lines are perpendicular to horizontal lines. Notes: x y 2 4 2 2 2 y 2x 2 y .
Skew Lines Skew lines are lines that are and do not . In this diagram, planes R and W are parallel. DEand FGare lines. Perpendicular lines are not skew lines, because they're in the same . Parallel lines are skew lines,
Line 2 Form 990-EZ, Part I, Lines 2 and 6b Line 3 N/A (Zero Reported) Line 4 N/A (Zero Reported) Line 5 N/A (Zero Reported) Line 6 Total of Lines 1-5 Lines 7a-7c N/A (Zero Reported) Line 8 Total of Column F Section B Line 9 Bring down amount from Section A, Line 6 Line 10a Form 990-EZ
Look at each group of lines. Trace over any parallel lines with a coloured pencil: Lines, angles and shapes – parallel and perpendicular lines 1 2 3 Parallel lines are always the same distance away from each other at any point and can never meet. They can be any length and go in any direc on. ab c ab c Perpendicular lines meet at right angles.
Parallel and 3 Perpendicular Lines 3.1 Identify Pairs of Lines and Angles 3.2 Use Parallel Lines and Transversals 3.3 Prove Lines are Parallel 3.4 Find and Use Slopes of Lines 3.5 Write and Graph Equations of Lines 3.6 Prove Theorems About Perpendicular Lines In previous chapters, you learned the following skills, which you’ll use in
Identify the lines as parallel, perpendicular, or neither. Unit 1Identifying Intersecting, Perpendicular, and Parallel Lines Intersecting lines are lines that cross each other at one point, called the point of intersection. X is the point of intersection of lines LM and NO. Perpendicular lines are two lines that form a right angle at the
