Ch. 4 Definitions, Postulates, and Theorems
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trismalhotra on November 26, 2011
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49 terms
Terms | Definitions |
|---|---|
 Acute Triange | a triange that has three acute angles |
| Equiangular Triangle | A triangle with 3 congruent angles |
| Obtuse Triangle | a triangle with one obtuse angle |
| Right Triangle | a triangle with one right angle |
| Equilateral Triangle | a triangle with three congruent sides |
| Isosceles Triangle | A triangle with at least two congruent sides |
| Scalene Triangle | a triangle with no congruent sides |
| Auxiliary Line | An extra line or line segment drawn in a figure to help in a proof. |
| Exterior Angle | an angle formed by one side of a triangle and the extension of another side |
| Remote Interior Angles | the two nonadjacent interior angles corresponding to each exterior ange of a triangle |
| Flow Proof | a type of proof that uses arrows to show flow of a logical argument statements are connected by arrows to show how each statement comes before it. and each reason is written below the statement it justifies |
| Corollary | a theorem with a proof that follows as a direct result of another theorem |
| Congruent | Having the same size and shape |
| Congruent Polygons | two polygons whose corresponding sides and angles are congruent |
| Corresponding Parts | The parts of congruent figures that match. |
| Definition of Congruent Polygons | two triangles are congruent, if and only if their corresponding parts are equal. |
| Included Angle | the angle formed by two adjacent sides of a polygon |
| Included Side | a side included between 2 angles |
| Legs of an Isosceles Triangle | The congruent sides of the isosceles triangle |
| Vertex Angle | the angle between the two sides of equal length |
| Base Angles | the angles whose vertices are the endpoints of the base of the triangle |
| Transformation | an operation that maps an original geometric figure onto a new figure |
| Preimage | the original figure |
| Image | the new figure |
| Congruence Transformation | transformation changes the position of a figure without changing its size or shape |
| Isometry | same as a congruence transformation |
| Reflection | A transformation that "flips" a figure over a mirror or reflection line. |
| Translation | A transformation that "slides" each point of a figure the same distance in the same direction. |
| Rotation | A transformation that turns a figure about a fixed point at a given angle and a given direction. |
| Coordinate Proof | proof that uses figures in the coordinate plane & algebra to prove geometric concepts. |
| Placing Triangles on a Coordinate Plane | Step 1: Use origin as vertex Step 2: Place at least one side on an axis Step 3: Keep triangle in the first quadrant Step 4: Use simple coordinates |
| SSS Congruence | when three sides of one triangle are congruent to three sides of another triangle |
| SAS Congruence | 2 sides, 1 angle |
| ASA Congruence | two triangles are congruent if two angles and the included side of one triangles are congruent, respectively, to two angles and the included side of the other |
| Triangle Angle-Sum | the rule that all angles of a triangle must add up to 180˚ |
| Exterior Angle Theorem | measure of the exterior angle is equal to the sum of the remote interior angles |
| Triangle Angle-Sum Corollary #1 | the acute angles of a right angle are complementary |
| Triangle Angle-Sum Corollary #2 | there can be at most one right or obtuse angle in a triangle |
| Third Angle Theorem | If 2 angles of 1 triangle are congruent to 2 angles of a second triangle then the third angles of the triangles are congruent |
| Properties of Triangle Congruence | Reflexive, Symmetric, and Transitive Properties |
| AAS Congruence | If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles are congruent. |
| Leg-Leg Congruence | If the legs of one right triangle are congruent to the corresponding legs of another right triangle, then the triangles are congruent |
| Hypotenuse-Angle Congruence | If the hypotenuse and acute angle of one right triangle are congruent to the hypotenuse and corresponding acute angle of another right triangle, then the two triangles are congruent. |
| Leg-Angle Congruence | 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 triangles are congruent. |
| Hypotenuse-Leg Congruence | if the hypotenuse and a leg of a right triangle are congruent to the hypotenuse of another right triangle then the right triangle then the triangle are congruent |
| Isosceles Triangle Theorem | If two sides of a triangle are congruent, then the angles opposite those sides are congruent |
| Converse of Isosceles Triangle Theorem | if two angles of a triangle are congruent, then the sides opposite those angles are congruent |
| Equilateral Triangle Corollary #1` | a triangle is equilateral iff it is equiangular |
| Equiangular Triangle Corollary #2 | each acute angle of an equiangular triangle is 60 degrees |
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