# GEOMETRY VOLUME AND SURFACE AREA FORMULAS

## 33 terms

Ph

L + 2B

2πrh + 2πr^2

1/2Pl + B

πrl + πr^2

4πr^2

Bh

πr^2h

(1/3)Bh

(1/3)πr^2h

(4/3)πr^3

(N/360)πr^2

### Third Angle Theorem

If 2 angles of one triangle are congruent to two angles of a second triangle, the third angles of the triangle are congruent.

### Circumcenter Theorem

The circumcenter of a triangle is equidistant from the vertices

### Incenter Theorem

THe incenter of a triangle is equidistant from each side of the triangle

### Centroid Theorem

The centroid of a triangle is located two thirds of the distance from a vertex to the midpoint of the side opposite the vertex on a median

### Circumcenter

Point of concurrency of perpendicular bisectors

### Incenter

point of concurrency of angle bisectors

### Centroid

Point of concurrency for the medians of a triangle

### Orthocenter

intersection point of altitudes

### Isosceles Triangle Theorem

If 2 sides of a triangle are congruent, then the angles opposite those sides are congruent

### SSS Similarity

if the measure of the corresponding sides of 2 triangles are proportional, then the triangles are similar

### SAS Similarity

If the measure of 2 sides of a triangle are proportional to the measure of 2 corresponding sides of another triangle, and the included angles are congruent, then the triangles are similar

### Triangle Proportionality Theorem

If a line is parallel to one side of a triangle and intersects the other 2 sides in 2 distinct points, then it separates these sides into segments of proportional lengths

### Proportional Perimeters Theorem

If 2 triangles are similar, then the perimeters are proportional to measure of corresponding sides

### Angle Bisector Theorem

An angle bisector in a triangle separates the opposite side into segments that have the same ratio as the other 2 sides

### Law of Sines

(sin A)/a = (sin B)/b = (sin C)/c

### Law of Cosines

a^2 = b^2 + c^2 - 2bc cos A

### Parallelogram

Diagonals bisect, opposite sides congruent, consecutive angles supplementary, opposite angles congruent, one pair of opposite sides parallel and congruent

### Rectangle

Same properties as parallelogram, diagonals are congruent

### Rhombus

Diagonals are perpendicular, Each diagonal bisects 2 angles

### Arc Length

(A/360) = (l/(2πr))

### Equation of a circle

(x - h)^2 + (y - k)^2 = r^2