Geometry

Question 1

Basic Approach

Answer 1

Draw the figure, label everything, write formulas

Question 2

Problem Solving: Can you trust the diagram?

Answer 2

Yes, they are to scale

Question 3

Data Sufficiency: Can you trust the diagram?

Answer 3

Trickier, may not match info in the statements..

Question 4

What are the Big 6?

Answer 4

Lines and Angles; Triangles; Quadrilaterals; Circles; 3D Shapes; Coordinate Geometry

Question 5

Passes through 2 points and goes on forever in both directions.

Answer 5

Line

Question 6

Starts at one point and goes on forever.

Answer 6

Ray

Question 7

Starts at one point and ends at another.

Answer 7

Line Segment

Question 8

Degrees in a line?

Answer 8

180

Question 9

Degrees in a circle?

Answer 9

360

Question 10

When two straight lines intersect, angles ___ each other are equal

Answer 10

Opposite (known as opposite or vertical angles)

Question 11

AB ⊥ CD means

Answer 11

Line AB is perpendicular to Line CD

Question 12

AB ∥ CD means

Answer 12

Line AB is parallel to Line CD

Question 13

When a third line intersects two parallel lines, two angles are formed: ___ angles and ___ angles.

Answer 13

big; small

Question 14

Any big angle + any small angle =

Answer 14

180 degrees

Question 15

In a paralllelogram, rule of ____ & _____ applies

Answer 15

big angle & small angle (big + small = 180)

Question 16

In triangles, there is a direct relationship between _____ & _____

Answer 16

Angle measure & side length

Question 17

Special Triangles on GMAT are (3):

Answer 17

equilateral, isoceles, right

Question 18

Because isosceles triangles have two equal sides, the angles ______ those sides are ______

Answer 18

opposite; equal

Question 19

Pythagorean Theorem

Answer 19

a^2 + b^2 = c^2; only in right triangles

Question 20

Pythagorean Triples

Answer 20

3:4:5 - 5:12:13 (and their multiples, ie: 6:8:10)

Question 21

Special Right Triangles

Answer 21

45-45-90 & 30-60-90 angles

Question 22

Sides of Isosceles Right Triangle Ratio

Answer 22

45:45:90 have sides of a:a:a*sqrt(2)

Question 23

Half of Equilateral Triangle Ratio

Answer 23

30:60:90 have sides of a:a*sqrt(3):2a

Question 24

When you see an equilateral triangle…

Answer 24

Remember you can always create two 30-60-90 triangles by drawing the height (ie: find area from the perimeter of the triangle)

Question 25

Third Side Rule (triangles)

Answer 25

difference of the other 2 sides < third side < sum of the other two sides (ex: sides of 3, 5, 9 are impossible)

Question 26

Area of a triangle

Answer 26

A = 1/2(b)(h) -- base and height must be perpendicular

Question 27

Rule of 360 degrees

Answer 27

Any four sided figure's angles make up 360 degrees

Question 28

Parallelogram's Area

Answer 28

always base x height, height must be perpendicular to base

Question 29

What is a chord?

Answer 29

Line from one point on the circumference of the circle to another

Question 30

What is an arc?

Answer 30

A piece of a circle (so the length of an arc is a portion of the circumference)

Question 31

Circumference =

Answer 31

Pi*d or 2*Pi*r

Question 32

Area of a circle =

Answer 32

Pi*r^2

Question 33

What is a sector?

Answer 33

a fraction of the area of a circle (a "pie slice")

Question 34

Central Arc Formula (proportions in a circle)

Answer 34

Central angle/360 = arc/circumference = sector/area

Question 35

What is a central angle?

Answer 35

An angle formed by the intersection of two radii at the center of a circle