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The sum of the angles in a triangle always equal?
180
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The perimeter of a triangle is the sum of:
- the length of its sides
- a+b+c = # (perimeter)
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Area of triangle formula?
- Base * Height / 2
- A = B*H/2
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The height/altitude of a triangle is always perpendicular to the...
base
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The longest side of a triangle is always the side...
opposite the greatest angle
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The shortest side of a triangle is always the side...
opposite the smallest angle
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A right angle triangle is defined by what? And what calculation allows you to calculate the length of one side if you know the other two sides?
Right angle triangle = has one angle equal to 90 deg
- Pythagorean Theorem
- a2 + b2 = c2
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What are the two most common values (or ratio of) used on the GMAT for right triangles & their side lengths?
3,4,5 or 5,12,13
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Two other very common right triangles are?
- 30/60/90
- & 45/45/90 (AKA Right Isosceles Triangle)
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30/60/90 Triangles always have sides in what proportions?
1, √3, 2 or x, x√3, 2x
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For any right triangle you need how many sides to solve for another side?
Need 2 sides to solve for 1
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In a 30/60/90 triangle 2x = short, med, or long side? And where is located?
2x = longest side & is always opposite the 90 degree (on the hypotenuse)
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In a 30/60/90 triangle x = short, med, or long side? And where is located?
x (or 1) = short. Always opposite the 30 deg. angle
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In a 30/60/90 triangle x√3 = short, med, or long side? And where is located?
x√3 = med side. Always opposite the 60° angle
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a 45/45/90 triangle always has sides with lengths of the proportion...
1, 1, and √2 or x, x, x√2
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What's the definition of an Isosceles Triangle?
Has at least two sides and two angles that are the same.
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What in an isosceles triangle creates two equal triangles? And how?
The altitude splits the base & the angle evenly when drawn from the unequal side. Creating two congruen (equal) triangles on each side.
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What's the definition of an Equilateral triangle? What's it also considered?
Definition: All sides are equal length & all angles are 60°. Also is considered an Isosceles triangle.
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When you take the height of an equilateral triangle (split in two) you form what?
two 30/60/90 triangles.
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What is the height of an equilateral triangle equal to?
- √3 times the side of the triangle
- 2
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Area of an equilateral triangle?
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If you have an equilateral triangle split into a 30/60/90 triangle what are the proportions?
- 30° side (x) = s/2
- 60° side (x√3) = (s√3)/2
- 90° side (2x) = s
s = side
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Whenever a supplementary angle is drawn off of an interior angle of a triangle - it will always equal the sum of the other two interior angles of the triangle.
c° + d° = 180
a°+b°+c°=180
thus: a°+b° = d°
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What's a similar triangle?
- All the angles are the same and the proportion of the corresponding sides & heights are constant.
- Little Triangle Sides = a,b,c
- Large Triangle Sides = 2a, 2b, 2c (for ex)
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What are the 3 standard ways to identify triangles that are similar?
1) AAA (angle, angle, angle) if 2 or 3 angles match b/w triangles, they are similar.
2) SSS (side, side, side) if there is a constant ratio of corresponding sides, they are similar.
3) SAS (side, angle, side) if there is a constant ratio of corresponding sides for 2 sets of sides AND the angle between those two sides is the same as the other triangle, they are similar.
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What is the property of any triangle involving the lengths of its sides?
The sum of any two lengths is greater than the length of the third side.
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What's the relationship b/w 2 sides of a triangle vs. the third side?
The sum of the two smaller sides has to be greater than the third side.
- ex: Side a = 2, Side b = 3, Side c = 4
- 2+3 > 4
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