2 7 Study Guide And Intervention Parallel Lines And Transversals

2 7 Study Guide And Intervention Parallel Lines And Transversals 1 1 Name Points Lines and PlanesIn geometry a pointis a location a linecontains points and a planeis a flat surface that contains points and lines If points are on the same line they are collinear If points on are the same plane they are coplanar Use the figure to name each of the following a a line containing point A

NAME DATE PERIOD O 3 5 Study Guide and Intervention Proving Lines Parallel Identify Parallel Lines If two lines in a plane are cut by a transversal and certain conditions are met then the lines must be parallel 7 4 Study Guide and Intervention Parallel Lines and Proportional Parts Proportional Parts within Triangles In any triangle a line parallel to one side of a triangle separates the other two sides proportionally This is the Triangle Proportionality Theorem The converse is also true If XY RS then RX XT SY YT

2 7 Study Guide And Intervention Parallel Lines And Transversals

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Identify the transversal connecting each pair of angles 1 9 and 13 2 5 and 14 3 4 and 6 Classify the relationship between each pair of angles as alternate interior alternate exterior corresponding or consecutive interior angles 4 1 and 5 5 6 and 14 6 2 and 8 7 3 and 11 8 12 and 3 9 4 and 6 10 6 and 16 11 11 and 14 12 10 and 16 q

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2 7 Study Guide And Intervention Parallel Lines And Transversals

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2 7 Study Guide And Intervention Parallel Lines And Transversals

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Parallel Lines and Angle Pairs When two parallel lines are cut by a transversal the following pairs of angles are congruent corresponding angles alternate interior angles alternate exterior angles Also consecutive interior angles are supplementary Example In the figure m 2 75 Find the measures of the remaining angles

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2 7 Study Guide and Intervention Parallel Lines and Transversals

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2 7 Study Guide and Intervention Parallel Lines and Transversals Transversal Angle Pair Relationships A line that intersects two or more other lines at two different points in a plane is called a transversal In the figure below line t is a transversal Two lines and a transversal form eight angles Some pairs of the angles have special names

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Parallel Lines and Transversals Relationships Between Lines and Planes When two lines lie in the same plane and do not intersect they are parallel Lines that do not intersect and are not coplanar are skew lines In the figure is parallel to m or m You can also write PQ RS

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Study Guide and Intervention Parallel Lines and Proportional Parts Proportional Parts within Triangles In any triangle a line parallel to one side of a triangle separates the other two sides proportionally This is the Triangle Proportionality Theorem The converse is also true If XY RS then RX XT SY If YT RX XT

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Parallel Lines that do not intersect and are not coplanar are skew lines In the figure is parallel to m or m You can also write PQ RS Similarly if two planes do not intersect they are parallel planes Example a Name all planes that are parallel to plane ABD plane EFH b Name all segments that are parallel to CwGw B wF


Study Guide and Intervention continued Proving Lines Parallel Prove Lines Parallel You can prove that lines are parallel by using postulates and theorems about pairs of angles m r s 12 43 56 87 910 12 11 13 14 16 15 Given 1 2 1 3 Prove AB DC Proof Statements Reasons 1 1 2 1 3 1 Given 2 2 3 2 3 2 Parallel Lines and Angle Pairs When two parallel lines are cut by a transversal the following pairs of angles are congruent corresponding angles alternate interior angles alternate exterior angles Also consecutive interior angles are supplementary In the figure m 2 5 75 Find the measures of the remaining angles m 1 5 105

NAME DATE PERIOD 2 7 Study Guide and Intervention continued Parallel Lines and Transversals Parallel Lines and Angle Pairs When two parallel lines are cut by a transversal the following pairs of angles are congruent corresponding angles alternate int