Term
|
Definition
|
|
Term
|
Definition
slope= rise/run or y2-y1/x2-x1 |
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
| segment addition postulate |
|
Definition
| if B is between A and C, then AB+BC= AC |
|
|
Term
|
Definition
formed by given hypothesis and concusion sybol p→q. Example: if two angles have the same measure, then they are congruent. |
|
|
Term
|
Definition
exchanging th hypothesis and conclusion of the conditional. symbol: q→p. Example: If two angles are congruent, then they have the same measure. |
|
|
Term
|
Definition
Negating both the hypothesis and conclusion of the conditional. Symbol: not p→not q example: If two angles do not have the same measure, then they are not congruent. |
|
|
Term
|
Definition
negating both the hypothesis and conclusion of the converse statement. symbol: not q→not p. Example: If two angles are not congruent, then they do not have the same measures. |
|
|
Term
| Angle Adddition Postulate |
|
Definition
| if R is in the interior of <PQS, then m<PQR + m<RQS= m<PQS |
|
|
Term
|
Definition
| Angles supplementary to the same angle or to congruent angles are congruent. |
|
|
Term
|
Definition
| Angles complementary to the same angle or to congruent angles are congruent. |
|
|
Term
|
Definition
| perpendicular lines intersect to form four right angles |
|
|
Term
|
Definition
| All right angles are congruent |
|
|
Term
|
Definition
| Perpendicular lines form congruent adjacent angles |
|
|
Term
|
Definition
| If two angles are congruent and supplementary, then each angle is a right angle |
|
|
Term
|
Definition
| If two congruent angles form a linear pair, then they are right angles. |
|
|
Term
| Perpendicular Transversal Therom |
|
Definition
| In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendiular to the other. |
|
|
Term
|
Definition
| The sum of the measures of the angles of a triangle is 180 degrees. |
|
|
Term
|
Definition
| If two angles of one triangle are congruent to two angles of a second triangle then the third angles of the triangles are congruent. |
|
|
Term
|
Definition
| The measure of an exterior angle of a triangle is equal to the sum of the two remote interior angles. |
|
|
Term
Side and Angle triangle congruence |
|
Definition
|
|
Term
| Congruence in right triangles |
|
Definition
LL- leg leg congruence HA- Hypotenuse angle congruence LA- Leg angle congruence HL- hypotenuse leg congruence |
|
|
Term
| Isosceles triangle theorem |
|
Definition
| If two sides of a triangle are congruent, then the angles opposite those sides are congruent |
|
|
Term
| Converse of Isosceles Triangle Theorem |
|
Definition
If two angles of a triangle are congruent, then the sides opposite those angles are congruent. |
|
|
Term
|
Definition
| The circumcenter of a triangle is equidistant from all vertices of a triangle |
|
|
Term
|
Definition
- Any point on the angle bisector is equidistant from the sides of the angle.
- Any point equidistant from the sides of an angle lies on the angle bisector
|
|
|
Term
|
Definition
segment whose endpoints are a vertex of a triangle and the midpoint of the side opposite the vertex on the median. point of concurrency: Centroid |
|
|
Term
|
Definition
| The centroid of a triangle is located 2/3 if the distance from a vertex to the midpoint of the side opposite the vertex on a median. |
|
|
Term
|
Definition
segment from a vertex to the line containing the opposite side and perpendicular to the line containing that side. point of concurrency: orthocenter |
|
|
Term
| Exterior Angle Inequality Theorem |
|
Definition
If an angle is an exterior angle of a triangle, then its measure is greater then the measure of either of its corresponding remote interior angles. |
|
|
Term
|
Definition
If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side. |
|
|
Term
|
Definition
| If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle. |
|
|
Term
| Triangle Inequality Theorem |
|
Definition
The sum of the lengths of any two sides of a triangle is greater than the length of the third side. |
|
|
Term
|
Definition
| the perpendicular segment from a point to a plane is the shortest segment from the point to the plane. |
|
|
Term
Side and Angle Triangle Inequality |
|
Definition
|
|
Term
| Side and Angle similarity |
|
Definition
|
|
Term
| Triangle Proportionality Theorem |
|
Definition
| If a line is parallel to one side of a triangle and intersects the other two sides in two distinct points, then it seperates these sides into segments of proportional lengths. |
|
|
Term
| Converse of Triangle Proportionality Theorem |
|
Definition
| If a line intersects two sides of a triangle and seperates the sides into corresponding segments of proportional lengths, then the line parallel to the third side |
|
|
Term
| Triangle Midsegment Theorem |
|
Definition
| A midsegment of a triangle is parallel to one side of a triangle and its length is 1/2 length of that side. |
|
|
Term
| Three parallel lines cut by a transversal theorem (1) |
|
Definition
| If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally. |
|
|
Term
Three parallel lines cut by a transversal corollary (2) |
|
Definition
| If three or more parallel lines cut off congruent segments on one transversal, they cut off congruent segments on all transversals. |
|
|
Term
| Special Segments on Similar Triangles |
|
Definition
- Similar triangles have corresponding altitudes proportional to corresponding sides.
- Similar triangles have corresponding angle bisectors proportional to corresponding sides.
- Similar triangles have corresponding medians proportional to corresponding sides.
|
|
|
Term
| Proportional Perimeter Theorem |
|
Definition
If two triangles are similar, then the perimeters are proportional to the measures of the corresponding sides. |
|
|
Term
|
Definition
| An angle bisector in a triangle seperates the opposite side into segments that have the same ratio as the other two sides. |
|
|
