| A | B |
|---|
| Angle Sum Theorem | The sum of the measure of the angles of a triangle is 180 degrees. |
| Third Angle Theorem | If two angles of one triangle are congruent to two angles of a second triangle, the the third angles of the triangles are congruent as well. |
| Exterior Angle Theorem | The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. |
| Corollary 4-1: The Relationship of the Acute Angles of A Right Triangle | The acute angles of a right triangle are complementary. |
| Corollary 4-2: Number of Right and Obtuse Angles in a Triangle | There can be at most one right or obtuse angle in a triangle. |
| Corollary 4-4: Types of Congruences Between Triangles | Congruence of triangle is reflexive, symmetric, and transitive. |
| SSS Postulate | If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. |
| SAS Postulate | If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. |
| ASA Postulate | If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. |
| Theorem AAS | If two angles and a nonincluded side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two tianagles are congruent. |
| Theroem 4-5: Isosceles Triangle Theorem | If two sides of a triangle are congruent, then the angles opposite are also congruent.. |
| Theorem 4-7: Congruency Relationships Between Angles and Sides | If two angles of a triangle are congruent, then the sides opposite thoses angles are congruent as well. |
| Corollary 4-3: The Relationship Between Equilateral and Equiangular Triangles | A triangle is equilateral if and only if it is equiangular. |
| Corollary 4-4: Angles of Equilateral Triangles | Each angle of an equilateral triangle measures 60 degrees. |
| Theorem 5-1: Perpendicular Bisectors of Line Segments | A point on the perpendicualr bisector of a segment is equidistant from the endpoints of the segment. |
| Theorem 5-2: Perpendicular Bisectors of Line Segments | A point equidistant from the endpoints of a segment lies on the perpendicular bisector of the segment. |
| Theorem 5-3: Angles Bisectors and Equidstant Sides | A point on the bisector of an angle is equidistant from the sides of the angle. |
| Theorem 5-4: Interior Angles and Angle Bisectors | A point on or in the interior of an angle adn equidistant from the sides of an angle lies on the bisector of the angle. |
| Theorem 5-5: The LL Right Triangle Theorem | If the legs of one right triangle are congruent to the corresponding legs of another right triangle, then the triangles are congruent. |
| Theorem 5-6: The HA Right Triangle Theorem | If the hypotenuse and an 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. |
| Theorem 5-7: The LA Right Triangle Theorem | If one leg and and an acute angle of one right triangle are congruent to the corresponding leg and acute angle of another triangle, The the triangles are congruent. |
| Postulate 5-1: The HL Right Triangle Postulate | If the hypotenuse and a leg of one triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent. |
| Theorem 5-8: Exterior Angle Inequality Theorem | 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. |
| Theorem 5-9: The Relationship Between the Measures of the Sides and Angles of a Triangle | 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. |
| Theorem 5-10: The Relationship Between the Measures of the Angles and Sides of a Triangle | 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. |
| Theorem 5-11: The Perpendicular Segment From A Point | The perpendicular segment from a point to a line is the shortest segment from the point to the line. |
| Corollary: 5-1: Perpendicular Segment-Point-Plane | The perpendicular segment from a point to a plane is the shortest segment from the point to the plane |
| Theorem 5-12: Triangle Inequality Theorem | Teh sum of the lenghts of any two sidess of a triangle is greater than the lenght of the third (3rd) side. |
| Theorem 5-13: SAS Inequality Theorem (The Hinge Theorem) | If two sides of one triangle are congruent to two sides of another triangle, and the included angle in one triangle is greater than the included angle in the other, then the third (3rd) side of the first triangle is longer than the third (3rd) side in the second triangle. |
| Theorem 5-14: SSS Inequality Theorem | If two sides of one triangle are congruent to two sides of another triangle and the third (3td) side in one triangle is longer than the third (3rd) side in the other, then the angle between the pair of congruent sides in the first triangle is greater than the corresponding angle in the second triangle. |
| Theorem 8-1: Altitude of a Right Triangle | If the altitude is drawn from the vertex of the right angle of a right triangle to its hypotenuse, then the two (2) triangles formed are "similar" to the given triangle and to each other. |
| Theorem 8-2: Altitude and Geometric Mean of Right Triangles - Two Segments | The measure of the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse. |
| Theorem 8-3: Altitude and Geometric Mean of Right Triangles - Adjacent Leg | If the altitude is drawn to the hypotenuse of a right triangle, then the measure of a leg of the triangle is the geometric mean between the measures of the hypotenuse and the segment of the hypotenuse adjacent to the leg. |
| Theorem 8-4: Pythagorean Theorem | In a right triangle, the sum of the squares of the measures of the legs equal the square of the measures of the hypotenuse. |
| Theorem 8-5: Converse of the Pythagorean Theorem | If the sum of the squares of the measures of two sides of a triangle equals the square of the measure of the longest side, then the triangle is a right triangle. |
| Theorem 8-6: 45-45-90 Degree Right Triangle | In a 45-45-90 degree right triangle, the hypotenuse is the $ \sqrt [2]{2}$ times as long as a leg. |
| Theorem 8-7: 30-30-90 Degree Right Triangle | In a 30-30-90 degree right triangle, the hypotenuse is twoice as long as the shorter leg, and the longer leg is $ \sqrt [2]{3}$ times as loong as the shorter leg. |
| Define: Equiangular Triangle | An equiangular triangle is one whose three (3) angles are congruent. |
| Define: Equilateral Triangle | An equilaterqal triangle is one whose three (3) sides are congruent. |
| Define: Acute Triangle | An acute triangle is one whose three (3) angles all measure under 90 degrees. |
| Define: Right Triangle | A right triangle is one that has one angle that is equal to 90 degrees. |
| Define: Obtuse Triangle | An obtuse triangle is one in which one of the angles is over 90 degrees and less than 180 degrees. |
| Define: Base of a Triangle | The base of a triangle is the side of the triangle in which the triangle rests. |
| Define: The Legs of a Triangle | The legs of a triangle are the two sides of a triangle other than the base side. |
| Define: Vertex Angle of a Triangle | The vertex angle is the one formed by both legs of a triangle. |
| Define: Base Angles of a Triangles | The base angles of a triangle are the two angles on each side of the base side of the given triangle. |
| Define: An Exterior Angle of a Triangle | An exterior angle of a given triangle is a angle that is outside of the triangle and forms a linear pair (is supplemental) with one of the interior angles of the given triangle. |
| Define: m Internal Angles of a Triangle | An internal angle of a triangle is one of the three (3) inside angles that make up a given triangle. |
| What is SSS? | Congruency of triangles based on "side-side-side" congruences. |
| What is SAS? | Congruency of triangles based on "side-angle-side" congruences. |
| What is ASA? | Congruency of triangles based on "angle-side-angle" congruences. |
| What is AAS? | Congruency of triangles based on "angle-angle-side" congruences. |
| Define: Corollary | a corollary is a proposition that follows with little or no proof required from one already proven |
| List three (3) characteristic special to 30-30-90 degree right triangles. | They are the following: 1) The leg opposite the 30 degree angle is 1/2 the hypoptenuse 2) The leg opposite the 60 degree angle is 1/2 the hypotenuse times the $ \sqrt [2]{3}$ 3) An altitude in an equilateral triangle forms a 30-30-90 degree right triangle and is therefore equal to 1/2 the hypothenuse times the $ \sqrt [2]{4}$ |
| List three (3) characteristic special to 45-45-90 degree right triangles. | They are the following: 1) Each leg is 1/2 the hypotenuse times the $ \sqrt [2]{3}$ 2) hyupotense is leg times the $ \sqrt [2]{2}$ 3) The diagonal ina square forms a 45-45-90 degree right triangle and is therefore equal to a side times the $ \sqrt [2]{2}$ |
