CH 3 Guided Notes page 2,3 1 Identify Pairs of Lines and Angles. Term Definition Example,parallel lines,parallel to. not parallel to,skew lines,parallel planes,What is a Named. Postulate 13 If there is a line and a point not on the line. Parallel Postulate then there is exactly one line through the. point parallel to the given line, Postulate 14 If there is a line and a point not on the line. Perpendicular then there is exactly one line through the. Postulate point perpendicular to the given line, transversal The lines the transversal intersects do not. need to be parallel the transversal can also,be a ray or line segment. CH 3 Guided Notes page 3,Special Angles formed by Transversals. corresponding,consecutive,interior angles,consecutive. exterior angles,CH 3 Guided Notes page 4,3 2 Use Parallel Lines and Transversals. Term Definition Example, Postulate 15 If two parallel lines are cut by a transversal then. Corresponding the pairs of corresponding angles are congruent. Angles Postulate Proof Abbrieviation, Theorem 3 1 If two parallel lines are cut by a transversal then. Alternate the pairs of alternate interior angles are. Interior Angles congruent,Theorem Proof Abbrieviation. Theorem 3 2 If two parallel lines are cut by a transversal then. Alternate the pairs of alternate exterior angles are. Exterior Angles congruent,Theorem Proof Abbrieviation. Theorem 3 3 If two parallel lines are cut by a transversal then. Same Side the pairs of Same Side Interior AKA Consecutive. Interior Angles Interior angles are supplementary,Theorem Proof Abbrieviation. BONUS Theorem If two parallel lines are cut by a transversal then. Same Side the pairs of Same Side Exterior angles are. Exterior Angles supplementary,Theorem Proof Abbrieviation. CH 3 Guided Notes page 5,3 3 Prove Lines are Parallel. Term Definition Example, Postulate 16 If two lines are cut by a transversal so the. Corresponding corresponding angles are congruent then the lines. Angles Converse are parallel,not named Proof Abbrieviation. Theorem 3 4 If two lines are cut by a transversal so the. Alternate alternate interior angles are congruent then the. Interior Angles lines are parallel,Converse Proof Abbrieviation. Theorem 3 5 If two lines are cut by a transversal so the. Alternate alternate exterior angles are congruent then the. Exterior Angles lines are parallel,Converse Proof Abbrieviation. Theorem 3 6 If two lines are cut by a transversal so the Same. Same Side Side Consecutive Interior angles are, Interior Angles supplementary then the lines are parallel. Converse Proof Abbrieviation, BONUS Theorem If two parallel lines are cut by a transversal then. Same Side the pairs of Same Side Exterior angles are. Exterior Angles supplementary,Converse Proof Abbrieviation. paragraph proof,CH 3 Guided Notes page 6, If two lines are parallel to the same line then they. Theorem 3 7 are parallel to each other,Transitive,Property of. Parallel Lines,CH 3 Guided Notes page 7,3 4 Find and Use Slopes of Lines. Term Definition Example,positive slope,negative slope. zero slope,slope of zero,no slope A horizontal line. undefined slope,A vertical line,In a coordinate plane two nonvertical lines. Postulate 17 are parallel if and only if they have the. Slopes of same slope,Parallel Lines,Any two vertical lines are parallel. In a coordinate plane two nonvertical lines,are perpendicular if and only if the product. Postulate 18 of their slopes is 1, Perpendicular The slopes of the two lines that are. Lines perpendicular are negative reciprocals of,each other Horizontal lines are. perpendicular to vertical lines, if and only if The form used when both a conditional and. form its converse are true,CH 3 Guided Notes page 8. 3 5 Write and Graph Equations of Lines,Term Definition Example. slope intercept,standard form,x intercept,y intercept. CH 3 Guided Notes page 9,Chap3 Constructing Parallel Perpendicular Lines. Remember that the complete construction guide all 7 Basic constructions has been. posted online at www behmermath weebly com, 4 Construct the perpendicular bisector of a line segment. Or construct find the midpoint of a line segment,1 Begin with line segment XY X Y. 2 Place the compass at point X Adjust the compass radius. so that it is more than XY Draw two arcs as shown,3 Without changing the compass radius place the A. compass on point Y Draw two arcs intersecting the, previously drawn arcs Label the intersection points. 4 Using the straightedge draw line AB Label the, intersection point M Point M is the midpoint of line A. segment XY and line AB is perpendicular to line,segment XY. CH 3 Guided Notes page 10, 5 Given a point P ON a line k construct a line through P perpendicular to k. 1 Begin with line k containing point P k, 2 Place the compass on point P Using an arbitrary radius k. draw arcs intersecting line k at two points Label the X P Y. intersection points X and Y, 3 Place the compass at point X Adjust the compass radius. so that it is more than XY Draw an arc as shown,4 Without changing the compass radius place the A. compass on point Y Draw an arc intersecting the, previously drawn arc Label the intersection point A. 5 Use the straightedge to draw line AP Line AP is,perpendicular to line k A. CH 3 Guided Notes page 11, 6 Given a point R NOT ON a line k construct a line through R perpendicular to k. 1 Begin with point line k and point R not on the line R. 2 Place the compass on point R Using an arbitrary radius R. draw arcs intersecting line k at two points Label the Y. intersection points X and Y, 3 Place the compass at point X Adjust the compass radius R. so that it is more than XY Draw an arc as shown Y,4 Without changing the compass radius place the R. compass on point Y Draw an arc intersecting the Y, previously drawn arc Label the intersection point B. 5 Use the straightedge to draw line RB Line RB is,perpendicular to line k. CH 3 Guided Notes page 12, 7 Given a line a point not on the line construct a line through the point parallel to the given line. 1 Begin with point P and line k P,2 Draw an arbitrary line through point P. intersecting line k Call the intersection point Q,Now the task is to construct an angle with vertex. P congruent to the angle of intersection,3 Center the compass at point Q and draw an arc. intersecting both lines Without changing the,radius of the compass center it at point P and. draw another arc,4 Set the compass radius to the distance between. the two intersection points of the first arc Now,center the compass at the point where the second. arc intersects line PQ Mark the arc intersection,point R Q k. 5 Line PR is parallel to line k,CH 3 Guided Notes page 13. 3 6 Prove Theorems about Perpendicular Lines,Term Definition Example. If two lines intersect to form a linear pair, Theorem 3 8 of congruent angles then the lines are. not named perpendicular,If two lines are perpendicular then they. Theorem 3 9 intersect to form four right angles,If two sides of two adjacent acute angles. Theorem 3 10 are perpendicular then the angles are. not named complementary, Theorem 3 11 If a transversal is perpendicular to one of. Perpendicular two parallel lines then it is perpendicular to. Transversal the other, Theorem 3 12 In a plane if two lines are perpendicular to. Lines the same line then they are parallel to each. Perpendicular to other,a Transversal,distance from a.

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