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Definition
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Term
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Definition
| A quadrilateral with both pairs os opposite sides parallel |
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Term
| Properties of parallelogram |
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Definition
- both pairs of sides parallel
- both pairs of opposite sides congruent
- Both pairs of opposite angles congruent
- consecutive angles supplementary
- diagonals bisect eachother |
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Term
| properties of a rectangle |
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Definition
- 90 degree angles
- diagonals bisect eachother
- all the properties of the parallelogram |
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Term
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Definition
| a quadrilateral with four right angles |
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Term
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Definition
| a quadrilateral with four congruent sides |
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Definition
- diagonals are perpendicular
- diagonals bisect opposite angles
- all the properties of a parallelogram |
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Term
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Definition
| a quadrilateral with four right angles and four congruent sides |
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Term
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Definition
| - all properties of rhombus, rectangle, and parallelogram |
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Term
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Definition
| a quadrilateral with exactly one pair of parallel sides |
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Definition
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Definition
The median of a trapeziod is parallel to the bases and its measure is half the sum of the measures of the bases
median=1/2(upper base + lower base)
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Term
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Definition
| A quadrilateral is a kite if an only if it has two distinct pairs of adjacent congruent sides |
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Term
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Definition
- one diagonal bisects the other
- one pair of opposite angles are congruent
- one pair of opposite angles are bisected |
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Term
| The five ways to prove a quadrilateral a parallelogram |
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Definition
1) If both pairs of opposite sides of a quadrilateral are parallel
2) If both pairs of opposite sides of a quad are congruent
3) If both pairs of opposite angles are congruent
4) If the diagonals bisect eachother
5) If one pair of opposote sides are both parallel and congruent |
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Term
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Definition
| a line or a line segment that passes through the midpoint of a triangle and is perpindicular to that side |
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Term
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Definition
| a segment drawn froma vertex of a triangle to the midpoint of the opposite side of that vertex |
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Term
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Definition
| a segment drawn from a vertex of a triangle perpendicular to the opposite side of that vertex |
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Term
| perpendicular bisector theorem |
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Definition
| if 2 points are equidistant from the endpoints of a segment, then they form a perpendicular bisector |
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Term
| converse of perpendicular bisector theorem |
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Definition
| If a point is on the perpendicular bisector of a segment, then that point is equidistant from the endpoints of the segment. |
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Term
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Definition
| if congruent segments, then equidistant points |
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Term
| converse equidistant theorem |
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Definition
| If equidistant points, then congruent segments. |
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Term
| median reason (for proofs) |
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Definition
| If median, then intersects midpoint. |
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Term
| perpendicular bisector reason (for proof) |
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Definition
| If perpendicular bisector, then divides a segment into two congruent segments and forms right angles. |
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Term
| altitude reason (for proof) |
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Definition
| If altitude, then perpendicular. |
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Term
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Definition
| A segment that bisects an angle of the triangle (one endpoint at a vertex and the other endpoint at another point on the triangle.) |
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Term
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Definition
• Any point on the bisector of an angle is equidistant from the sides of the angle.
• Any point on or in the interior of an angle and equidistant form the sides of an angle lies on the bisector if the angle.
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Term
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Definition
| If the legs of one right triangle are congruent to the corresponding legs of another right triangle, then the triangles are congruent. |
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Term
| HA (hypotenuse-angle) theorem |
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Definition
| If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and angle of another right triangle, then the two triangles are congruent. |
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Term
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Definition
| If one leg and an acute angle of one right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the two triangles are congruent. |
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Term
| HL (Hypotenuse-leg) postulate |
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Definition
| If the hypotenuse and the leg of one right triangle are congruent to the hypotenuse and the corresponding leg of another right triangle, then the 2 triangles are congruent. |
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Term
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Definition
| A proof that leads to the conclusion by proving all other possibilities impossible. Indirect proofs can be written in 2 column or paragraph form. |
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Term
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Definition
| If an angle is an exterior angle of a triangle, then its measure is greater than the measure of either of its corresponding remote interior angles. |
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Term
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Definition
| For any real numbers a and b, a>b if and only if there is a positive number c such that a=b+c |
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Term
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Definition
• If one side of triangle is longer than another, than the angle opposite the longer side is greater than the angle opposite the shorter side
• If an angle of a triangle is greater than another, then the side opposite the greater angle is longer that the side opposite the lesser angle. |
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Term
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Definition
If two sides of one triangle are congruent to two sides of another triangle and the included angle in the second triangle, then the remaining side of the first triangle is greater than the remaining side of the second triangle.
Abbreviation: Hinge theorem (SAS ≠) |
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Term
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Definition
If 2 sides of one triangle are congruent to 2 sides of another triangle and the third side of the first triangle is greater than the third side of the second triangle, then the angle opposite the third side in the first triangle is greater than the angle opposite the third side in the second triangle.
Abbreviation: Converse Hinge Theorem (SSS ≠) |
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Term
| Triangle Inequality Theorem |
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Definition
| The sum of the lengths of any two sides of a triangle is greater than the length of the third side. |
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Term
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Definition
| A triangle with one obtuse angle (or more than 90 degree angle) |
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Term
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Definition
| A triangle with one angle being 90 degrees. |
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Term
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Definition
| Acute triangle in which all angles are congruent (all 60 degrees) |
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Term
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Definition
| All angles in triangle are less than 90 degrees |
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Term
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Definition
| A triangle with no two congruent sides |
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Term
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Definition
| All sides of triangle are congruent |
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Term
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Definition
| A triangle with at least two congruent sides |
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Term
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Definition
| The sum of the measures of the angles of a triangle is 180 degrees. |
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Term
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Definition
| The measure of an angle of a triangle is equal to the sum of the measures of the two remote interior angles. |
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Term
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Definition
| A statement that can be easily proven using a theorem |
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Term
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Definition
| The acute angles of a right triangle are complimentary |
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Term
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Definition
| There can be at most one right or obtuse angle in a triangle |
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Term
| Congruence of Triangle theorem |
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Definition
| Congruence of triangles is reflexive, symmetric, and transitive. |
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Term
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Definition
| If all three corresponding sides of two triangles are congruent, then the triangles are congruent. |
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Term
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Definition
| If 2 sets of corresponding sides AND the INCLUDING angle of two triangles are congruent, then the triangles are congruent. |
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Term
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Definition
| If 2 sets of corresponding triangles and the included measure of 2 triangles are congruent, then the triangles are congruent. |
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Term
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Definition
| If 2 angles and a non included side of one triangle are congruent to the corresponding 2 angles and the side of the second triangle, then the 2 angles are congruent. |
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Term
| Isosceles Triangle Theorem |
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Definition
| If 2 sides of a triangle are congruent, then the angles opposite those sides are congruent. |
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Term
| Converse Isosceles Triangle Theorem |
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Definition
| If 2 angles of a triangle are congruent, then the sides opposite those angles are congruent. |
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Term
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Definition
| A triangle is equilateral if and only if it is equiangular. |
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Term
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Definition
| Each angle of an equiangular triangle measures 60 degrees. |
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Term
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Definition
| Two lines in a plane that never meet |
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Term
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Definition
| Two lines that don't intersect and aren't in the same plane. |
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Term
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Definition
| A line that intersects two or more lines in a plane at different points. |
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Term
| Corresponding angles postulate |
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Definition
| If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent. |
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Term
| Alternate interior Angles Theorem |
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Definition
| If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent. |
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Term
| Consecutive Interior Angles Theorem |
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Definition
| If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary. |
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Term
| Alternate Exterior Angle Theorem |
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Definition
| If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent. |
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Term
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Definition
| In a plane, if a line is perpendicular to one of tow parallel lines, then it is perpendicular to the other. |
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Term
| Ways to prove parallel lines |
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Definition
1) If alternate exterior angles are congruent, then parallel lines.
2) If alternate interior angles congruent, then parallel lines.
3) If consecutive interior angles supplementary, then parallel lines
4) If two lines perpendicular to the same lines, then parallel lines.
5) If 2 lines are parallel to the same line, then they are parallel |
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Term
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Definition
| If there is a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line. |
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Term
| Definition of Distance Between a Point and a Line |
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Definition
| The distance from a line to a point not on the line is the length of the segment perpendicular to the line from the point. |
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Term
| Definition of Distance Between Parallel Lines |
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Definition
The distance between two parallel lines is the distance between one of the lines and any point on the other line.
Two lines that are parallel in a plane are EVERYWHERE EQUIDISTANT |
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Term
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Definition
An educated guess based on observations of a particular situation.
May be true or false!! |
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Term
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Definition
| An example that proves the conjecture false |
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Term
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Definition
A way of thinking in which conclusions are justified by previously assumed or proved statements
Geometry is based on Deductive structures
Based on:
• undefined terms
• postulates
• definitions
•theorems
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Term
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Definition
| Look at several specific situations to arrive at a conjecture. |
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Term
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Definition
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Term
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Definition
| Reverse hypothesis and conclusion. If q, then p. (q→p) |
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Term
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Definition
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Term
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Definition
| ~p (not p)
ex: p: it is raining
negation (not p): It is not raining |
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Definition
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Term
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Definition
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Term
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Definition
| Points that lie on the same line |
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Definition
| a statement that is assumed to be true |
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Term
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Definition
| an angle is made up of 2 rays with a common vertex |
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Term
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Definition
| Angles that have a common vertex and a common side, but no common interior points |
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Term
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Definition
| Adjacent angles whose non common sides are opposite rays |
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Term
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Definition
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Term
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Definition
| Set of elements that overlap or are shared |
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