Geometry Lecture Notes: Triangles, Polygons, Transformations, Proofs, and Volumes

A set of QUESTION_AND_ANSWER style flashcards covering triangles, polygons, transformations, proofs, and volumes based on the provided lecture notes.

What is the sum of the interior angles of a triangle?

180 degrees

According to the exterior angle theorem for triangles, an exterior angle equals the sum of which interior angles?

The two remote interior angles (the two interior angles not adjacent to the exterior angle).

What is the sum of exterior angles for any polygon?

360 degrees (one exterior angle at each vertex).

Triangle inequality theorem states that in any triangle, the sum of the lengths of any two sides is greater than what?

The length of the remaining side.

State the Pythagorean theorem for a right triangle.

a^2 + b^2 = c^2, where c is the hypotenuse.

Name the common triangle congruence criteria.

SSS, SAS, AAS, and HL (for right triangles).

Name the similarity criteria for triangles.

AA, SAS, SSS.

Sum of interior angles of a polygon with n sides?

(n - 2) * 180 degrees.

Measure of each interior angle in a regular n-gon?

[(n - 2) * 180] / n degrees.

Sum of exterior angles of a polygon?

360 degrees.

What are the rigid motions (transformations) that preserve size and shape?

Translation, rotation, and reflection.

What transformation changes size by a scale factor k?

Dilation.

Volume formula for a prism with base area B and height h?

V = B × h.

Volume formula for a cylinder with radius r and height h?

V = pi * r^2 * h.

Volume formula for a cone with radius r and height h?

V = (1/3) * pi * r^2 * h.

Volume formula for a sphere?

V = (4/3) * pi * r^3.

Volume formula for a pyramid with base area B and height h?

V = (1/3) * B * h.

Distance formula between points (x1,y1) and (x2,y2)?

sqrt[(x2 - x1)^2 + (y2 - y1)^2].

Slope formula between two points (x1,y1) and (x2,y2)?

m = (y2 - y1) / (x2 - x1).

What do L, W, and H stand for in a prism?

Length, Width, and Height.

Two common proof styles in geometry?

Two-column proofs and paragraph proofs (and coordinate proofs).

Which proof style uses coordinates to prove a statement?

Coordinate proof.