Definition of Perpendicular lines (IMPORTANT): Two lines that intersect to form RIGHT ANGLES! A line perpendicular to a plane is a line that intersects the plane in a point that is perpendicular to every line in the plane that intersects it. All definitions work __________ and ___________ If two lines are perpendicular, then they form a ___________. If two lines intersect to form ________________, then they are perpendicular. 2.2 – Definitions and Biconditional Statements

All definitions work forwards and backwards If two lines are perpendicular, then they form a right angle. If two lines intersect to form right angles, then they are perpendicular. If a conditional statement and its converse are both true, it is called biconditional, and you can combine them into a “if and only if” statement

True or false? Why? (Check some hw) Z Y X W V U T S R WVZ and RVS form a linear pair. YVU and TVR are supplementary Y, V, and S are collinear WVT and YVX are complementary.

Write the conditional statement and the converse as a biconditional and see if it’s true. If two segments are congruent, then their lengths are the same. If the lengths of the segments are the same, then they are congruent.

Write the conditional statement and the converse as a biconditional and see if it’s true. If B is between A and C, then AB + BC = AC If AB + BC = AC, then B is between A and C

Write the converse of the statement, then write the biconditional statement. Then see if the biconditional statement is true or false. (Check more hw) If x = 3, then x 2 = 9 If two angles are a linear pair, then they are supplementary angles.

Split up the biconditional into a conditional statement and its converse. Pizza is healthy if and only if it has bacon. Students are good citizens if and only if they follow the ESLRs.

Warm – Up: Graph the following 4 equations. y = 0 x = 0 y = x y = -x 2.4 – Reasoning with Properties from Algebra

Reasons

Reflexive Prop. Of equality Symmetric Prop. Of equality Transitive Prop. Of equality

We will fill in the blanks MATH 1) 2) 3) 4) 5) 1) 2) 3) 4) 5)

D U C K 1 2 1) 2) 3) 4) 5) 1) 2) 3) 4) 5)

A NG S E L

Copy a segment 1) Draw a line 2) Choose point on line 3) Set compass to original radius, transfer it to new line, draw an arc, label the intersection. 2.6 – Proving Statements about Angles

__________ Property Symmetric Property _________ Property Right Angle Congruence Thrm - All ______ angles are _______

Congruent Supplements Theorem If two angles are ____________ to the same angle (or to congruent angles), then they are congruent. If _____ and _____ are supplementary and _____ and ____ are supplementary then ____ Congruent Complements Theorem If two angles are ____________ to the same angle (or to congruent angles), then they are congruent. If _____ and _____ are complementary and _____ and ____ are complementary then ____

Explain in your own words why congruent supplements theorem has to be true. This may show up on your test.

V ertical Angles Thrm - _____ angles are ______ Linear Pair Postulate – If two angles form a linear pair, then they are _________

W R I O Z S A L

E RA T Given Prove

Given Prove Def of Supp Angles

P KM N Given Prove J Number 2

V Q R T Substitution Prop = Given Prove P