Math: Unit 3
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- Parallel Lines
- Coplanar lines that do not intersect
- Skew lines
- Noncoplanar lines that are neither paralled nor intersecting
- Parallel planes
- Planes that do not intersect
- Theorem 3-1
- If two parallel planes are cut by a third plan, then the lines of intersection are parallel
- Postulate 10
- If two parallel lines are cut by a transversal, then corresponding angles are congruent.
- Theorem 3-2
- If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
- Theorem 3-3
- If two parallel lines are cut by a transversal, then same-side interior angles are supplementary.
- Theorem 3-4
- If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also.
- Postulate 11
- If two lines are cut by a transversal and correspond angles are congruent, then the lines are parallel.
- Theorem 3-5
- If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.
- Theorem 3-6
- If two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel.
- Theorem 3-7
- In a plan two lines perpendicular to the same line are parallel.
- Theorem 3-8
- Through a point outside a line, there is exactly one line parallel to the given line.
- Theorem 3-9
- Through a point outside a line, there is exactly one line perpendicular to the given line.
- Theorem 3-10
- Two lines parallel to a third line are parallel to each other.
- Scalene triangle
- None of the sides are congruent
- Isosceles triangle
- At least two of the sides are congruent
- Equilateral triangle
- All of the sides are congruent
- Acute triangle
- A triangle with three acute angles
- Obtuse triangle
- A triangle with one obtuse angle
- Right triangle
- A triangle with one right angle
- Equiangular triangle
- A triangle whose angles are all congruent
- Theorem 3-11
- The sum of the measures of the angles of a triangle is 180
- Corollary 1
- If two angles of one trianble are congruent to two angles of another triangle, then the third angles are congruent.
- Corollary 2
- Each angles of an equiangular triangle has measure 60.
- Corollary 3
- In a triangle, there can be at most one right angle or obtuse angle.
- Corollary 4
- The acute angles of a right triangle are complementary.
- Theorem 3-12
- The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles.
- Polygon
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1. Each segment intersects exactly 2 other segments, one at each endpoint
2. No 2 segments within a common endpoint are collinear - Convex polygon
- Polygon in which no line containing a side of the polygon contains a point in the interior of the polygon
- Theorem 3-13
- The sum of the measures of the angles of a convex polygon with n sides is (n-2)180
- Theorem 3-14
- The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex, is 360
- Regular polygon
- Polygon that is both equiangular and equilateral