Bellwork Solve for x & y if m & n are parallel Clickers Bellwork Write the converse of the statement: If two lines are perpendicular, then they intersect at a right angle Use the diagram to complete the following Two Alternate Interior Angles are ________________ Two Corresponding Angles are ___________ Two Consecutive Interior Angles are _____________ Solve for x & y if m & n are parallel 1 2 3 4 5 6 7 8 n x y 65 55 m

Bellwork Write the converse of the statement: If two lines are perpendicular, then they intersect at a right angle If two lines are not perpendicular, then they do not intersect at a right angle If two lines do not intersect at a right angle, then they are not perpendicular If two lines intersect at a right angle, then they are perpendicular

Bellwork Use the diagram to complete the following Two Alternate Interior Angles are 1 2 3 4 5 6 7 8 4 & 6 4 & 8 1 & 8 4 & 5

Bellwork Use the diagram to complete the following Two Corresponding Angles are 1 2 3 4 5 6 7 8 4 & 6 4 & 8 1 & 8 2 & 5

Bellwork Use the diagram to complete the following Two Consecutive Interior Angles are 1 2 3 4 5 6 7 8 4 & 6 4 & 8 1 & 8 2 & 5

Bellwork Solve for x & y, if m & n are parallel 45,55 65, 60 60, 60 90, 45 m

Prove Lines are Parallel Section 3.3

The Concept Yesterday we learned about the Theorems that rule Parallel Lines Today we’re going to see the converses of these statements and their implications

Dilemma Using the ruler, draw this diagram If I wanted to draw another line parallel to the bottom one, what would I do? θ θ Axis of symmetry Vertex

The Converses We can use the converse of the theorems that we learned yesterday to prove that two lines are in fact parallel We do this by setting up our equations like normal, but instead of assuming parallel lines, we find the values that make things parallel What value of x makes these two lines parallel? 5x-25 145 Axis of symmetry Vertex

Converse Postulates & Theorems Postulate 16: Corresponding Angles Converse If two lines are cut by a transversal so that the corresponding angles are congruent, then the lines are parallel Theorem 3.4: Alternate Interior Angles Converse If two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel Theorem 3.5: Alternate Exterior Angles Converse If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel Theorem 3.6: Consecutive Interior Angles Converse If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel Postulate 15: Corresponding Angles Postulate If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent Theorem 3.1: Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent Theorem 3.2: Alternate Exterior Angles Theorem If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent Theorem 3.3: Consecutive Interior Angles Theorem If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary Vertex

In Use 25 30 50 Solve for x, given lines a & b are parallel 6x a b 150 Axis of symmetry Vertex

In Use 25 27 54 What value of x makes lines a and b parallel? 2x-4 a b 50 Axis of symmetry Vertex

In Use 3.5 10 13 What value of x makes lines a and b parallel? 2x+10 a Axis of symmetry Vertex

In Use 55 125 18 What value of x, will make lines a and b parallel a x Axis of symmetry Vertex

In Use 5 28 140 What value of x, will make lines a and b parallel a 5x Axis of symmetry Vertex

In Use 20 30 60 What value of x, will make lines a and b parallel 60 a Axis of symmetry Vertex

In Use 5 20 40 What value of x, will make lines a and b parallel a 4x 160 b Axis of symmetry Vertex

Definition Before we go too much further we need to discuss the Law of Syllogism within a geometric context Transitive Property A similarity between two items can be transferred to the third, if that same similarity is shared with the last two items e.g. Axis of symmetry Vertex

Another one Without looking: What does the transitive property of parallel lines mean? A B C Theorem 3.7 Transitive Property of Parallel Lines If two lines are parallel to the same line, then they are parallel to each other Axis of symmetry Vertex

In Use What is the value of x, a & b are parallel and b &c are parallel a 5x 9 27 45 b 135 c Axis of symmetry Vertex

Homework 3.3 1, 2, 5-9, 18-32 even, 40-44

Most Important Points Terminology for lines cut by a transversal Theorems regarding parallel lines cut by a transversal