## 54 terms · Geo Exam-Fall

### triangle inequality theorem

the sum of the lentghs of any 2 sides of a triangle is greater than the length of the third side

### triangle side comparison theorem

if 2 angles of a triangle are not congruent, then the longer side lies opposite the larger angle

### triangle angle comparison theorem

if 2 sides of a triangle are not congruent, then the larger angle lies opposite the longer side

### hinge theorem

if 2 sides of 1 triangle are congruent to 2 sides of another triangle, but the included angle of the first triangle is larger than the included angle of the second trianlge, then the third side of the first triangle is greater than the third side of the second triangle

### SAS postulate

if 2 sides and the included angle of 1 triangle are congruent to 2 sides and the included angle in a second triangle, then the 2 triangles are congruent.

### third angle theorem

if 2 angles of 1 triangle are congruent to 2 angles in a second triangle, then their third angles are also congruent

### HL theorem

if the hypotenuse and leg of 1 right triangle are congruent to the hypotenuse and leg of a second right triangle, then the 2 triangles are congruent

### SSS postulate

if 3 sides of 1 triangle are congruent to 3 sides of a second triangle, then the 2 triangles are congruent.

### triangle exterior angle theorem

the exterior angle of a triangle is equal to the sum of its corresponding remote interior angles

### isosceles triangle theorem

if two sides of a triangle are congruent, then the angles opposite those sides are congruent

### AAS theorem

if 2 angles and a non-included side of 1 triangle are congruent to 2 angles and a non-included side in a second triangle, then the 2 triangles are congruent

### theorem

in a coordinate plane, 2 nonvertical lines are perpendicular iff their slopes are negative reciprocals of each other

### corresponding angles postulate

if a transversal intersects 2 parallel lines, then the corresponding angles are congruent

### alternate interior angles theorem

if a transversal intersects 2 parallel lines, then the alternate interior angles are congruent

### same side interior angles theorem

if a transversal intersects 2 parallel lines, then the same side interior angles are supplementary

### Law of Detachment

if a conditional statement is true and its hypothesis is true, then its conclusion is true.

### segment addition postulate

if a, b, and c are collinear points and b is betewwn a and c, then AB+BC=AC

### angle bisector theorem

if BX (--> over) is the bisector of <ABC, then m<ABX=1/2 m<ABC and m<XBC=1/2 m<ABC

### congruent supplements theorem

if 2 angles r supplementary to the same (or congruent angles), then the 2 angles are congruent.

### congruent complements theorem.

if 2 angles r complementary to the same (or congruent angles), then the 2 angles are congruent.

### converse of the corresponding angles potulate

if the corresponding angles are congruent, then the transvesal intersects 2 parallel lines

### converse of the alternate interior angles theorem

if the alternate interior angles are congruent, then the transvesal intersects 2 parallel lines

### converse of the same side interior angles theorem

if 2 lines and a transveral form same side interior angles that are supplementary, then the 2 lines are parallel

### converse of the alt. ext. angles theorem

if the alt. ext. angles are congruent, then the transvesal intersects 2 parallel lines

### ASA postulate

if 2 angles and the included side of 1 triangle are congruent to 2 angles and the included side of a second triangle, then the 2 triangles are congruent

### angle bisector theorem

if a point is on the angle bisector of an angle, then it is equidistant from the 2 sides of the triangle