list of all geometry theorems?

Check out the GMAT Math Study sheet. It contains all the formulas needed for the test.

I know I'm digging up an old post here, but the above link goes to nothing....

So, does anybody happen to have a list of all the geometry theorems we could possibly see on the test?

When I get a geometry data sufficiency problem wrong on a practice CAT it is usually because of some theorem I didn't remember...

WilliamGCash wrote: ↑

Wed Nov 03, 2010 12:59 pm

I know I'm digging up an old post here, but the above link goes to nothing....

So, does anybody happen to have a list of all the geometry theorems we could possibly see on the test?

When I get a data sufficiency problem wrong on a practice CAT it is usually because of some theorem I didn't remember...

Here’s a compact list of key geometry theorems you’ll commonly need: Pythagorean Theorem (and special right triangles 45-45-90, 30-60-90, 5-12-13), Triangle Sum Theorem, Exterior Angle Theorem, Isosceles Triangle Theorem, Similarity Theorems (AA, SAS, SSS), Triangle Inequality, Heron’s Formula, Area formulas (triangle ½bh, equilateral √3/4 a²), Law of Sines, Law of Cosines, Midsegment Theorem, Angle Bisector Theorem, Ceva’s and Menelaus’ Theorems, Parallel Line angle theorems, Polygon interior/exterior angle sums, Circle Theorems (inscribed angle, central angle, tangent–secant, chord theorems), Power of a Point, Thales’ Theorem, Coordinate geometry distance/midpoint/slope formulas, and basic transformations (reflection, rotation, translation, dilation).

Here is a breakdown of the core geometry rules, theorems, and shortcuts that cover around 95% of what you will ever need for standard math tests:

Triangles (The Most Tested Category)

* Pythagorean Theorem: a^2 + b^2 = c^2 (for right-angled triangles only).
* Common Pythagorean Triplets: Memorize 3-4-5, 5-12-13, 8-15-17, and 7-24-25 (plus their multiples like 6-8-10 or 10-24-26).
* Special Right Triangles:
* 30-60-90 Triangle: Side ratio is 1 : sqrt(3) : 2 (opposite to 30°, 60°, and 90° respectively).
* 45-45-90 Triangle: Side ratio is 1 : 1 : sqrt(2).


* Triangle Inequality Theorem: The third side must be greater than the difference of the other two sides and less than their sum.
* Exterior Angle Theorem: The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.
* Similar Triangles: Corresponding sides are proportional. If the ratio of sides between two similar triangles is a:b, their area ratio is a^2 : b^2.

Circles

* Area & Circumference: Area = pi * r^2 and Circumference = 2 * pi * r.
* Arc Length: (Central Angle / 360) * 2 * pi * r.
* Sector Area: (Central Angle / 360) * pi * r^2.
* Inscribed Angle Theorem: An inscribed angle (vertex on the circle) is always half the measure of its central angle on the same arc.
* Angle in a Semicircle: Any triangle inscribed in a circle where one side is the diameter is a 90-degree right triangle.
* Tangent Line Rule: A line tangent to a circle meets the radius at a right angle (90 degrees).

Polygons & Lines

* Sum of Interior Angles: (n - 2) * 180 degrees (where n is the number of sides).
* Parallel Lines & Transversals: Alternate interior angles are equal; interior angles on the same side add up to 180 degrees.

Coordinate Geometry

* Distance Formula: sqrt((x2 - x1)^2 + (y2 - y1)^2) — which is just the Pythagorean theorem in coordinate form.
* Slopes of Perpendicular Lines: They are negative reciprocals of each other (e.g., if one slope is 2/3, the perpendicular line's slope is -3/2).

If you memorize these key ones, you will be able to solve almost every geometry problem you encounter!