# Geometry Theorems and Postulates With Names

## 29 terms · Theorems/postulates with names

If B is between A and C, then AB + BC = AC

If point B lies in the interior of angle AOC, then m∠AOB + m∠BOC = m∠AOC

### SSS Postulate

3 sides of one triangle are congruent to 3 sides of another triangle => congruent

### SAS Postulate

2 sides + included ∠ of one triangle are congruent to 2 sides + included ∠ of another triangle => congruent.

### ASA Postulate

2 ∠s + included side congruent to 2 ∠s + included side of another triangle => congruent

### AA Similarity Postulate

2 ∠s of one triangle congruent to two ∠ of another triangle => similar

measure of arc formed by two adjacent arcs is the sum of the measures of the two arcs

### Area Congruence Postulate

two figures congruent => same area

area of region = sum of areas of its non-overlapping parts

### Midpoint Theorem

M is midpoint of AB => AM = AB/2, MB = AB/2

### Angle Bisector Theorem

BX bisects ∠ABC => m∠ABC = (m∠ABX)/2 = (m∠XBC)/2

### Vertical Angle Theorem

vertical angles are congruent

### Isosceles Triangle Theorem

2 sides of triangle are congruent => angles opposite those sides are congruent

### ITT Corollary (a)

equilateral triangle is equiangular

### ITT Corollary (b)

equilateral triangle as three 60-degree angles

### ITT Corollary (c)

bisector of vertex angle of an isosceles triangle is perpendicular to the base at its midpoint

### AAS Theorem

two angles and non-included side of one triangle are congruent to corr. parts of another triangle => congruent

### HL Theorem

hypotenuse and leg of one right triangle congruent to corr. parts of another right triangle => congruent

### Exterior Angle Inequality Theorem

measure of exterior angle of a triangle is greater than the measure of either remote interior angle

### Triangle Inequality

sum of the lengths of any two sides of a triangle is greater than the length of the third side

### SAS Inequality Theorem

two sides of one triangle congruent to two sides of another triangle; included angle of 1st triangle larger than included angle of 2nd => 3rd side of 1st triangle is longer than 3rd side of 2nd triangle

### SSS Inequality Theorem

two sides of one triangle congruent to two sides of another triangle, 3rd side of 1st is longer than 3rd side of 2nd => included ∠ of 1st > ∠ of 2nd

### SAS Similarity Theorem

angle of one triangle congruent to angle of another triangle, sides including those angles in proportion => similar triangles

### SSS Similarity Theorem

sides of two triangles in proportion => similar triangles

### Triangle Proportionality Theorem

line parallel to one side of triangle intersects other two sides => divides sides proportionally

### TPT Corollary

3 parallel lines intersect two transversals => divide transversals proportionally

### Triangle Angle-Bisector Theorem

ray bisects angle of triangle => divides opposite side into segments proportional to the other two sides

### 45-45-90 Theorem

hypotenuse = √2 times as long as a leg

### 30-60-90 Theorem

the hypotenuse is twice as long as the shorter leg, and the longest leg is √3 times as long as the shorter leg