Proofs – creating a proof journal.

Postulates to know Example: If AB = 3x, BC = 2x + 20, and AC = 10x, what is the value of x?

Definitions Definition of a midpoint – a point that divides a segment into two congruent segments. Segment bisector – a line, ray, or other figure that passes through the midpoint of a segment. Definition of an angle bisector – a ray (line or segment) that divides an angle into two congruent angles (splits the angle in half)

Postulates to know Example: If ∠PQR = 105˚, ∠PQS = 75˚, and ∠SQR = (3x)˚, what is the value of x?

Properties of Equality

Definitions Complementary Angles – two angles whose measures add up to 90˚ Supplementary Angles – two angles whose measures add up to 180˚ Linear Pair – a pair of adjacent angles whose non-common sides are opposite rays.

Theorems to know

Definitions Definition of Congruence – two figures are congruent if and only if one can be obtained from the other by a sequence of rigid motions (reflections, translations, and/or rotations)

Critical Definition Corresponding Parts of Congruent Figures are Congruent – if two figures are congruent, then corresponding sides are congruent and corresponding angles are congruent

Properties of Congruence

Critical Definition Vertical Angles – if two lines intersect, the angles formed opposite each other are called vertical angles. Additional definitions -Opposite: across from each other -Adjacent: next to

Proving Triangle Congruence Recall the following properties of congruence.

Triangle Congruence Theorems

Triangle Congruence Theorems

Definitions Included Angle – an angle that is in between two sides when discussing triangle congruency statements (such as the angle in SAS triangles). Included Side – a side that is in between two angles when discussing triangle congruency statements (such as the side in ASA triangles). Non-Included Side – a side that is not in between two angles when discussing triangle congruency statements (such as the side in AAS triangles).

ASA Triangle Congruence Theorem Given Reflexive Property of Congruence Given

Given ASA Triangle Congruence Theorem Given Vertical Angle Theorem Definition of a Midpoint

Do you following proofs from your book in your groups (finish for homework): Page 238, #7 Page 239, #9 Page 266, #27 Page 231, #13