Similar Shapes, Congruence, Prism Volumes

volume + area of a cone

V: 1/3 * πr² h

A: πr² + πrl

frustum

when the tip of a cone is excluded

• volume = cone - smaller cone

volume + area of a pyramid

V: base area * h / 3

A: base area + (# of faces * face area)

volume + area of a sphere

V: 4/3πr²

A: 4πr²

what is a prism?

3D object with same cross section throughout

volume + area of a prism

V: base area * length

A: (area of each face * # of each face) + 2(base area)

volume + area of a cylinder

V: πr²h

A: 2πrh(circumference + height) + 2πr² (2 faces)

area + circumference of an arc

A: degree/360 * πr²

C: degree/360 * 2πr

labelled circle

congruence

having identical size & shape

ASA (angle side angle)

SAS (side angle side)

SSS (side side side)

RHS (right-angle, hypoteneuse, side)

how to describe congruence

use geometry laws + name one of the 4 theorems above

similar shape

one shape is the enlargement of another

• corresponding angles are equal

• corresponding sides are increased by the same scale factor

how to calculate similar shape sides

1. find scale factor (larger/smaller side)

2. divide(large to small) // multiply(small to large) by scale factor

similar area & volume

1. assume the scale factor is simplified to ratio A:B

2. area = A²:B² // volume = A³:B³