# Chapter 4 Conjectures

## 11 terms

### C-15 Vertical Angles Conjecture If two angles are a pair of vertical angles,

then the angles are congruent.

### C-16a Linear Pair Conjecture If two angles are a linear pair of angles,

then the angles are supplemental.

### C-16b Congruent Supplemental Angles Conjecture If two angles are both congruent and supplemental,

then the angles are right angles.

### C-17 Parallel Lines Conjecture If parallel lines are cut by a transversal,

then corresponding angles, alternate interior angles, and alternate exterior angles are congruent.

### C-18 Parallel Line Converse Conjecture If two lines are cut by a transversal such that corresponding angles, alternate interior angles, and alternate exterior angles are congruent,

then the lines are parallel.

### C-19 Midpoint Conjecture If (x1, y1) and (x2, y2) are the coordinates of the endpoints of a segment, then...

[(x1 + x2)/2, (y1 + y2)/2] are the coordinates of the midpoint of the segment.

### C-20 Slope Conjecture If the coordinates of one point are (x1, y1) and the coordinates of another point are (x2 , y2) then...

the slope of the line through the points can be found using m = (y2 - y1)/(x2 - x1).

### C-21 Parallel Slope Conjecture Two distinct lines in a coordinate plane are parallel iff

their slopes are equal.

### C-22 Perpendicular Slope Conjecture Two distinct lines in a coordinate plane are perpendicular iff

their slopes are negative reciprocals.

### C-23 Linear Equation Conjecture If the graph of a line has a slope of m and a y-intercept of (0 , b), then...

the equation of the line can be written in the form
y = mx + b PT-SLOPE y = m(x - x1) + y1

### C-24 Centroid Coordinate Conjecture If triangle TRY has the coordinates T(a , d), R(b , e) and Y(c , f) then

the centroid of TRY has the coordinates [(a + b + c)/3 , (d + e + f)/3].