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1.
30-60-90 triangle: 30° --> 60° --> 90°

short leg --> long leg --> hypotenuse

1 -->√3 --> 2

short leg --> long leg --> hypotenuse

1 -->√3 --> 2

2.
Angles correspond to their opposite sides: 1) Largest angle is opposite the longest side.

2) Smallest angles is opposite the smallest side.

3) If two sides are equal, the opposite angles are equal.

2) Smallest angles is opposite the smallest side.

3) If two sides are equal, the opposite angles are equal.

3.
Area of a equilateral triangle: =s²√3/4

4.
Area of a right triangle: 1/2**leg **leg (or) 1/2 ** hypotensuse ** height from hypotenuse

5.
Deluxe Pythagorean theorem: d² = l² + b² + h² - Can be used to calculate the diagonal of a cuboid.

6.
Equilateral Triangle: All the sides of the triangle are equal in length

7.
If two similar triangles have corresponding side lengths in ratio a:b => area lengths are in ratio: a² : b²

8.
Impostor Triangles: A random triangle with one side equal to 3 and other side equal to 4 does not necessarily have a third side of length 5.

9.
Isosceles right triangle: Angle measures - 45:45:90

Ratio of lengths - 1:1:√2 ( leg : leg : hypotenuse).

Isosceles right triangles is exactly half of a square. => If a diagonal is provided you can calculate sides.

Ratio of lengths - 1:1:√2 ( leg : leg : hypotenuse).

Isosceles right triangles is exactly half of a square. => If a diagonal is provided you can calculate sides.

10.
Isosceles Triangle: a triangle with two equal sides and consequently two equal angles opposite to the two sides

11.
Pythagoras Theorem: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides

12.
Pythagorean triples: 3,4,5; Multiple of 1

6,8,10 ; Multiple of 2

9,12,15 ; Multiple of 3

12,16,20 multiple of 4

5,12,13 ; 10,24,26

8,15,17;

6,8,10 ; Multiple of 2

9,12,15 ; Multiple of 3

12,16,20 multiple of 4

5,12,13 ; 10,24,26

8,15,17;

13.
Relation between diagonal of a cube and it's edge: d=s√3

14.
Relation between diagonal of a square and side: d = s√2

15.
Sides of a triangle property: Sum of any two sides of a triangle is always greater than the third side. If you are given two sides of a triangle, the length of the third side must lie between the difference and sum of the two given sides.

16.
Similar Triangles: 1) Corresponding angles are equal

2) Lengths of corresponding sides are in proportion

2) Lengths of corresponding sides are in proportion

17.
Sum of the angles of a triangle =: 180

## GMAT Triangles and Diagonals StrategyStudy online at quizlet.com/_4ahaw |

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