Geometry — GRE General Questions

6 GRE General practice questions on Geometry, part of Quantitative Reasoning. Below are 6 of them in full, each with the answer and a written explanation.

Questions & explanations

1. When using the exterior angle theorem, the exterior angle equals the sum of the two remote interior angles. This can help find missing angles without solving for all interior angles.

For example, if an exterior angle is 120° and one remote interior angle is 50°, the other remote interior angle is 70°. This is faster than finding the adjacent interior angle first.

2. When dealing with triangle problems, always check if the triangle is special (30-60-90, 45-45-90) or if Pythagorean triples apply. Look for side ratios that match known patterns to save time.

Recognizing special triangles can simplify calculations. For example, if you see sides 3,4,5 or multiples, it's a right triangle. If angles are 30,60,90, sides are in ratio 1:√3:2.

3. The area of a parallelogram is base times height. For a rectangle, it's length times width. A rhombus area can be found as half the product of its diagonals. A square is side squared. A trapezoid area is half the sum of the bases times height.

Each quadrilateral has a specific area formula. Memorize them: parallelogram A = bh, rectangle A = lw, rhombus A = (d1*d2)/2, square A = s^2, trapezoid A = (b1+b2)h/2.

4. For similar triangles, set up proportions with corresponding sides. If triangles share an angle or have parallel lines, they are often similar. Use scale factor to find unknown sides.

Identify corresponding vertices. For example, if triangle ABC ~ triangle DEF, then AB/DE = BC/EF = AC/DF. If AB=4, DE=6, BC=5, then EF = (5*6)/4 = 7.5.

5. In problems involving angle bisectors, remember that the bisector divides the angle into two equal parts. If a bisector is involved, set the two resulting angles equal to each other. Combine with other relationships like linear pairs or vertical angles to solve for variables.

This technique is useful for multi-step problems where an angle bisector is combined with parallel lines or perpendicular lines.

6. For triangle inequality questions, remember that the sum of any two sides must exceed the third. To test if three lengths form a triangle, check the smallest two sum > largest. If not, no triangle.

This is a quick check. For example, sides 2,3,6: 2+3=5 < 6, so no triangle. Sides 5,6,10: 5+6=11 > 10, so triangle exists.

More Quantitative Reasoning topics

This page shows 6 of 6 questions on this topic. The full set, with progress tracking and five agent perspectives per question, is in the JupiteX app — browse the exam catalogue or browse the Learn library.