Parallel Lines and Transversals Chapter 3-1

Lesson 3-1 Ideas/Vocabulary Identify the relationships between two lines or two planes. Name angles formed by a pair of lines and a transversal. parallel lines consecutive interior angles alternate exterior angles alternate interior angles corresponding angles parallel planes skew lines transversal Preparation for Standard 7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. (Key) Lesson 3-1 Ideas/Vocabulary

Triangles are used to indicate // lines Parallel Lines // Two lines are // if they are coplanar and do not intersect. Triangles are used to indicate // lines

Skew Lines Lines that do not intersect but are not coplanar are called skew lines.

Parallel Planes Two planes that do not intersect.

Based on looks, find a line: // to AB and containing D  to AB and containing D Skew to AB and containing D Name the plane(s) that contain D and appear to be // to plane ABE 1. DC A D E H B C G F 2. AD 4. DCH or DGH or DCG 3. DH

Identify Relationships A. Name all planes that are parallel to plane AEF. Answer: plane BHG Lesson 3-1 Example 1a

Identify Relationships __ B. Name all segments that intersect AF. Answer: EF, GF, DA, and BA __ Lesson 3-1 Example 1b

Identify Relationships __ C. Name all segments that are skew to AD. Answer: FG, GB, EH, EC, and CH __ Lesson 3-1 Example 1c

A. Name a plane that is parallel to plane RST. B C D plane WTZ plane SYZ plane WXY plane QRX Lesson 3-1 CYP 1a

B. Name a segment that intersects YZ. XY WX QW RS A. B. C. D. Lesson 3-1 CYP 1b

C. Name a segment that is parallel to RX. B. C. D. ZW TZ QR ST Lesson 3-1 CYP 1c

D. Name a segment that is skew to TZ. __ RX ST XW QW __ ___ A B C D Lesson 3-1 CYP 1d

Transversal A line that intersects two or more coplanar lines at different points. t 1 2 3 4 5 6 7 8 t is a transversal

If the lines are extended, line v intersects lines u, w, x, and z. Identify Transversals A. BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line v is a transversal. Answer: If the lines are extended, line v intersects lines u, w, x, and z. Lesson 3-1 Example 2a

Identify Transversals B. BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line y is a transversal. Answer: lines u, w, x, z Lesson 3-1 Example 2b

Identify Transversals C. BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line u is a transversal. Answer: lines v, x, y, z Lesson 3-1 Example 2c

A. HIKING A group of nature trails is shown A. HIKING A group of nature trails is shown. Identify the sets of lines to which line a is a transversal. A B C D lines c, f lines c, d, e lines c, d, f lines c, d, e, f Lesson 3-1 CYP 2a

B. HIKING A group of nature trails is shown B. HIKING A group of nature trails is shown. Identify the sets of lines to which line b is a transversal. A B C D no lines lines c, f lines c, d, e, f lines a, c, d, e, f Lesson 3-1 CYP 2b

C. HIKING A group of nature trails is shown C. HIKING A group of nature trails is shown. Identify the sets of lines to which line c is a transversal. A B C D lines a, b lines a, b, d, e, f lines a, d, f lines a, b, e Lesson 3-1 CYP 2c

D. HIKING A group of nature trails is shown D. HIKING A group of nature trails is shown. Identify the sets of lines to which line d is a transversal. A B C D lines e, f lines a, b, f lines a, b, c, e, f lines a, b, c Lesson 3-1 CYP 2d

Corresponding Angles Two angles that occupy corresponding positions. t 1 and 5 are corresponding s t 1 2 3 4 5 6 7 8 2 and 6 are corresponding s 3 and 7 are corresponding s 4 and 8 are corresponding s

Alternate Interior Angles Two angles that lie between the two lines on opposite sides of the transversal. t 1 2 3 4 5 6 7 8 3 and 6 are Alt. Int. s 4 and 5 are Alt. Int. s

Alternate Exterior Angles Two angles that lie outside the two lines on opposite sides of the transversal. t 1 2 3 4 5 6 7 8 1 and 8 are Alt. Ext. s 2 and 7 are Alt. Ext. s

Consecutive Interior Angles Two angles that lie between the two lines on the same side of the transversal. t 1 2 3 4 5 6 7 8 3 and 5 are Consecutive Int. s 4 and 6 are Consecutive Int. s Sometimes called Same Side Interior Angles

Identify Angle Relationships A. Identify 7 and 3 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: corresponding Lesson 3-1 Example 3a

Identify Angle Relationships B. Identify 8 and 2 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: alternate exterior Lesson 3-1 Example 3b

Identify Angle Relationships C. Identify 4 and 11 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: corresponding Lesson 3-1 Example 3c

Identify Angle Relationships D. Identify 7 and 1 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: alternate exterior Lesson 3-1 Example 3d

Identify Angle Relationships E. Identify 3 and 9 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: alternate interior Lesson 3-1 Example 3e

Identify Angle Relationships F. Identify 7 and 10 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: consecutive interior Lesson 3-1 Example 3f

A. Identify 4 and 5. A B C D alternate interior alternate exterior corresponding consecutive interior Lesson 3-1 CYP 3a

B. Identify 7 and 9. A B C D alternate interior alternate exterior corresponding consecutive interior Lesson 3-1 CYP 3b

C. Identify 4 and 7. A B C D alternate interior alternate exterior corresponding consecutive interior Lesson 3-1 CYP 3c

D. Identify 2 and 11. A B C D alternate interior alternate exterior corresponding consecutive interior Lesson 3-1 CYP 3d

E. Identify 3 and 5. A B C D alternate interior alternate exterior corresponding consecutive interior Lesson 3-1 CYP 3e

F. Identify 6 and 9. A B C D alternate interior alternate exterior corresponding consecutive interior Lesson 3-1 CYP 3e

Practice 1 4 3 2 8 5 6 7 11 9 10 12

Homework pg. 144 12-19, 24-35, 41-44