Parallel Lines and Transversals Chapter 3 1 Identify

Parallel Lines and Transversals Chapter 3 -1

• 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 • parallel planes • alternate exterior angles • skew lines • alternate interior angles • transversal • corresponding angles 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)

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: 1. 2. 3. 4. // 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 C 1. DC B 2. AD D A F E 3. DH H 4. DCH or DGH or DCG G

Identify Relationships A. Name all planes that are parallel to plane AEF. Answer: plane BHG

Identify Relationships __ B. Name all segments that intersect AF. __ __ Answer: EF, GF, DA, and BA

Identify Relationships __ C. Name all segments that are skew to AD. __ __ __ Answer: FG, GB, EH, EC, and CH

A. Name a plane that is parallel to plane RST. A. plane A WTZ B. plane B SYZ C. plane C WXY D. plane D QRX

B. Name a segment that intersects YZ. A. XY B. WX C. QW D. RS

C. Name a segment that is parallel to RX. A. ZW B. TZ C. QR D. ST

D. Name a segment that __ is skew to TZ. __ A. RX A __ B. ST B ___ C. XW C ___ D. QW D

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

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.

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

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

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

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

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

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

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

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

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

Identify Angle Relationships B. Identify 8 and 2 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: alternate exterior

Identify Angle Relationships C. Identify 4 and 11 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: corresponding

Identify Angle Relationships D. Identify 7 and 1 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: alternate exterior

Identify Angle Relationships E. Identify 3 and 9 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: alternate interior

Identify Angle Relationships F. Identify 7 and 10 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: consecutive interior

A. Identify 4 and 5. A. alternate A interior B. alternate B exterior C. corresponding C D. consecutive D interior

B. Identify 7 and 9. A. alternate A interior B. alternate B exterior C. corresponding C D. consecutive D interior

C. Identify 4 and 7. A. alternate A interior B. alternate B exterior C. corresponding C D. consecutive D interior

D. Identify 2 and 11. A. alternate A interior B. alternate B exterior C. corresponding C D. consecutive D interior

E. Identify 3 and 5. A. alternate A interior B. alternate B exterior C. corresponding C D. consecutive D interior

F. Identify 6 and 9. A. alternate A interior B. alternate B exterior C. corresponding C D. consecutive D interior

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

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