# Our Conjectures

## 24 terms · Discovering Geometry

### Central Angle-Arc (A)

the measurement of a central angle is equal to the meausurement of the intercepted arc. (p. 71)

### Bisected Obtuse Angle Conjecture (B)

If an obtuse angle is bisected, then the two newly formed congruent angles are acute angles. (P. 115)

### Overlapping Segments Conjecture (C)

If segment AD has points A, B, C, and D in that order with segment AB ≅ segment CD then segment AC ≅ segment BD. (p. 116)

### Overlapping Angles Conjecture (D)

If points C and D lie in the interior of ∠APB and ∠APC ≅∠BPD, then ∠APD ≅∠CPB. (p. 118)

### Congruent Supplementary Angles Conjecture (E)

If two angles are congruent and supplementary, then the measure of angles are 90 degrees.

### Linear Pair Conjecture (C1)

If two angles form a linear pair, then the measures of the angles add up to 180°. (p. 122)

### Vertical Angle Conjecture (C2)

If two angles are vertical angles, then they are congruent. (p. 123)

### Corresponding Angles Conjecture (C3a)

If two parallel lines are cut by a transversal, then corresponding angles are congruent. (p. 129)

### Alternate Interior Angles Conjecture (AIA Conjecture) (C3b)

If two parallel lines are cut by a transversal, then alternate interior angles are congruent. (p. 129)

### Alternate Exterior Angles Conjecture (AEA Conjecture) (C3c)

If two parallel lines are cut by a transversal, then alternate exterior angles are congruent. (p. 129)

### Parallel Lines Conjecture (C3)

If two parallel lines are cut by a transversal, then corresponding angles are congruent, alternate interior angles are congruent, and alternate exterior angles are congruent. (p. 129)

### Converse of the Parallel Lines Conjecture (C4)

If two lines are cut by a transversal to form pairs of congruent corresponding angles, congruent alternate interior angles, congruent alternate exterior angles, then the lines are parallel. (p. 130)

### Perpendicular Bisector Conjecture (C5)

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints. (p. 150)

### Converse of the Perpendicular Bisector Conjecture (C6)

If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.

### Shortest Distance Conjecture (C7)

The shortest distance from a point to a line is measured along the perpendicular segment from the point to the line.

### Angle Bisector Conjecture (C8)

If a point is on the bisector of an angle, then it is equidistant from the sides of the angle.

### Angle Bisector Concurrency Conjecture (C9)

The three angle bisectors of a triangle are
concurrent (meet at a point).

### Perpendicular Bisector Concurrency Conjecture (C10)

The three perpendicular bisectors of
a triangle are concurrent.

### Altitude Concurrency Conjecture (C11)

The three altitudes (or the lines containing the altitudes) of a triangle are concurrent.

### Circumcenter Conjecture (C12)

The circumcenter of a triangle is equidistant from the vertices.

### Incenter Conjecture (C13)

The incenter of a triangle is equidistant from the sides.

### Median Concurrency Conjecture (C14)

The three medians of a triangle are concurrent.

### Centroid Conjecture (C15)

The centroid of a triangle divides each median into two parts so that the distance from the centroid to the vertex is twice the distance from the centroid to the midpoint of the opposite side.

### Center of Gravity Conjecture (C16)

The centroid of a triangle is the center of gravity of the triangular region.