2 2 Definitions and Biconditional Statements Definition of

2. 2 – Definitions and Biconditional Statements 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.

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

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

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.

2. 4 – Reasoning with Properties from Algebra Warm – Up: Graph the following 4 equations. y=0 x=0 y=x y = -x

Reasons

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

We will fill in the blanks M A T H 1) 1) 2) 2) 3) 3) 4) 4) 5) 5)

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

A L N G E S

2. 6 – Proving Statements about Angles 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.

_____ 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 ____