## Glossary of Geometry Midterm Info.

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- Theorem 1-1
- if two lines intersect, then they intersect in exactly one point

- Theorem 1-2
- Through a line and a point not in the line there is exactly one plane

- Theorem 1-3
- If two lines intersect, then exactly one plane contains the lines

- Theorem 2-1 (Midpoint Theorem)
- If M is the midpoint of (segment) AB, then AM=1/2AB and MB=1/2AB

- Theorem 2-2 (Angle Bisector Theorem)
- if (ray) BX is the bisector of angle ABC, then m(angle)ABX=1/2 m(angle)ABC and m(angle)XBC=1/2 m(angle)ABC

- Theorem 2-3
- Vertical angles are congruent

- Theorem 2-4
- If two lines are perpendicular, then they form congruent adjacent angles

- Theorem 2-5
- If two lines form congruent adjacent angles, then the lines are perpendicular

- Theorem 2-6
- If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary

- Theorem 2-7
- If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent

- Theorem 2-8
- If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent

- Theorem 3-1
- If two parallel planes are cut by a third plane, then the lines of intersection are parallel

- 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 tranversal, 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

- Theorem 3-5
- If two lines are cut by the 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 and lines are parallel

- Theorem 3-7
- In a plane 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

- Theorem 3-11
- The sum of the measures of the angles of a triangle is 180

- Theorem 3-11 Corollary 1
- if two angles of one triangle are congruent to two angles of another triangle, the the third angles are congruent

- Theorem 3-11 Corollary 2
- Each angle of an equiangular triangle has measure 60

- Theorem 3-11 Corollary 3
- In a triangle, there can be at most one right angle or obtuse angle

- Theorem 3-11 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

- 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

- Theorem 4-1 (Isosceles Triangle Theorem)
- If two sides of a triangle are congruent, then the angles opposite those sides are congruent

- Theorem 4-1 Corollary 1
- An equilateral triangle is also equiangular

- Theorem 4-1 Corollary 2
- An equilateral triangle has three 60 degree angles

- Theorem 4-1 Corollary 3
- The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint

- Theorem 4-2
- If two angles of a triangle are congruent, then the sides opposite those angles are congruent

- Theorem 4-2 Corollary 1
- An equiangular triangle is also equilateral

- Theorem 4-3 (AAS Theorem)
- If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent

- Theorem 4-4 (HL Theorem)
- If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent

- Theorem 4-5
- If a point lies on the perpendicular bisector of a segment, then the point is equidistant for the endpoints of the segment

- Theorem 4-6
- If a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment

- Theorem 4-7
- If a point lies on the bisector of an angle, then the point is equidistant from the sides of the angle

- Theorem 4-8
- If a point is equidistant from the sides of an angle. then the point lies on the bisector of the angle

- Theorem 5-1
- Opposite sides of a parallelogram are congruent

- Theorem 5-2
- Opposite angles of a parallelogram are congruent

- Theorem 5-3
- Diagonals of a parallelogram bisect each other

- Theorem 5-4
- If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram

- Theorem 5-5
- If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram

- Theorem 5-6
- If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallogram

- Theorem 5-7
- If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram

- Theorem 5-8
- if two lines are parallel, then all points on one line are equidistant from the other line

- Theorem 5-9
- If three parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal

- Theorem 5-10
- a line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side

- Theorem 5-11
- The segment that joins the midpoints of two sides of a triangle

(1) is parallel to the third side

(2) is half as long as the third side

- Theorem 5-12
- Diagonals of a rectangle are congruent

- Theorem 5-13
- The diagonals of a rhombus are perpendicular

- Theorem 5-14
- Each diagonal of a rhombus bisects two angles of the rhombus

- Theorem 5-15
- The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices

- Theorem 5-16
- If an angle of a parallelogram is a right angle, then the parallelogram is a rectangle

- Theorem 5-17
- If two consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus

- Theorem 5-18
- Base angles of an isosceles trapezoid are congruent

- Theorem 5-19
- The median of a trapezoid

(1) is parallel to the bases

(2) has a length equal to the average of the base lengths.