# C.P.C.T.C Find a pair of with parts you C.P.C.T.C Find a pair of with parts you are trying to prove are proving a bisector or angle bisector Corresponding Parts of a Congruent Triangles are Congruent Prove the two triangles are congruent by C.P.C.T.C corresp. parts are congruent proving lines are parallel or perpendicular les e 2 ang prove th s it bisect gruent. are con B CD prove A B B C E A M Statements 1) angles, 4) AMB CMB 4) A S A 5) AM MC 5) CPCTC 6) BM is a bisector of AC 7) Definition of a segment bisector B CD prove A C V B V E F D A Statements Reasons 1) BE DF, BE DF, 1) given CE AF 2)

4) AE + EF = CF + EF 5) AE = CF 6) 6) SAS 7) contained in the ? Prove those parts are by C.P.C.T.C (this proves the bisector) Lines are parallel Lines are perpendicular Show triangles are Are the angles in the alt. interior, corresponding, or alt. exterior angles of lines? Prove those parts are by C.P.C.T.C (this proves the bisector) Show triangles are Are the angles contained in and formed by the lines linear pairs? Prove those angles are by C.P.C.T.C (this proves you have right angles and lines must be parallel) Altitude 3 Every triangle has exactly ______ altitudes. al

The altitude is a perpendicular ____________ segment vertex from one ___________ to the other side. de u t ti You may need to extend the bottom in order to draw the altitude. A median is a segment from a vertex ______________ midpoint of the to the ___________ other side. Median me dia An altitude and median combined into one is a perpendicul ar bisector An altitude can be inside OR outside ___________ of a triangle. n Every triangle has exactly 3 medians and all 3 ______ ____________ intersect at a single point called a centroid.

Rolling Ball Challenge #1 1) What do you need to know? You need to find the value of x so you can determine what the measurement for angle (7x) is. This will tell you which way the horizontal line will tilt. 2) What do already know? Because we have parallel lines... angles (12x) and (12y +6) are congruent, alternate, interior angles. So... 12x=12y +6 Using algebra to solve for x we find x=(y+0.5) 3) Now what? Our parallel lines also tell us angle (8y) and angle(4x+10) are supplementary interior angles on the same side as a transversal. So... 8y + 4x+10 = 1800 You already know x so, substitute it in. 8y + 4(y+0.5) +10 = 180 Remember: x=(y+0.5) 8y+4y+2+10=180 solve for x 12y +12=180 x=(y+0.5) 12y=168 x=(14.5+0.5) y=14.5 x = 15 4) Now, back to the angle that determines tilt... (7x) <7x = 1050 105 but this is what our 7x angle would look like. Can you see how it would tilt 0 Lets think about this: This is what a horizontal line would look like. to the left?? 750