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Special Right Triangles
Isosceles Right Triangle:
The isosceles right triangle is also called the 45-45-90 triangle because of the measures of the angles.
Theorem: The 45-45-90 Triangle:
The hypotenuse of a 45-45-90 triangle is 2^½ times as long as a leg.
The Pythagorean Theorem
In a right triangle, the square of the hypotenuse is equal to the sum of
the squares of the legs.
c²= a²+ b²
Theorem:
Right Triangles
Theorem:
Triangles
Triangles Theorem:
The measured angles of a triangle sum up to 180°.
Corollary 1
If two angles of a triangle are congruent to two other angles from another triangle then, the third angles are congruent.
Corollary 2
The individual measured angles of an equiangular triangle is 60°.
Corollary 3
Triangles
Parallel Lines
Parallel Lines:( || means parallel)
Parallel lines are lines that do not intersect and are coplanar.
Skew lines:
Skew lines are lines that do not intersect and are not coplanar.
Properties of Parallel Lines:
Postulate:
If two parallel lines are intersected by a transversal, then the corresponding angles are congruent.
Theorem:
If two parallel lines are intersected by a transversal, then the alternate interior angles are congruent.
Theorem:
Parallel Lines
Vertical angles are two angles whose sides form two pairs of opposite rays. When two lines intersect, two pairs of vertical angles are formed.
Theorem:
Vertical angles are congruent:
Postulate: Angle Addition Postulate
Point B lies in the interior of ? XYZ, if and only if, m?XYB + m?BYZ = m?XYZÂ
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