| A | B |
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| A theorem you prove before the main theorem to make proving the main theorem easier is called a ? | lemma |
| If a line is perpendicular to a plane, then it is perpendicular to every ? that passes through the ? | line / point of intersection (foot) |
| The point of intersection of a line and a plane is called the ? | foot |
| A line is perpendicular to a plane if and only if it is perpendicular to ? that passes through the foot | every line |
| If B and C are each equidistant from P and Q, then every point between B and C is ? from P and Q | equidistant |
| State the Basic Theorem on Perpendicularity | If a line is perpendicular to each of 2 intersecting lines at their point of intersection, then it is perpendicular to the plane that contains them |
| If 2 sides of a triangle are of unequal length, then the angles opposite them are of ? and the ? angle is opposite the longer side | unequal measure / larger |
| State the Parts Theorem | IF D is a point on segment AB between A and B, then segment AB is greater than segment AD and segment AB is greater than segment DB. If D is a point on the interior of angle ABC, than the measure of angle ABC is greater than the measure of angle ABD and the measure of angle ABC is greater than the measure of angle DBC. |
| State the Exterior Angle Theorem | The measure of an exterior angle is greater than the measure of both its remote interior angles. |
| If one angle of a triangle is a right angle, then the other 2 angles must be ? | acute |
| The sum of the measures of any 2 angles of a triangle must be less than ? | 180 |
| State the Hypotenuse Leg Theorem | If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of a 2nd triangle, then the triangles are congruent |
| State the Hypotenuse Acute Angle Theorem | If the hypotenuse and an acute angle of one right triangle are congruent to the corresponding parts of a 2nd triangle, then the triangles are congruent |
| State the Leg Acute Angle Theorem | If a leg and an acute angle of one right triangle are congruent to the corresponding parts of a 2nd triangle, then the triangles are congruent |
| State the Leg Leg Theorem | If 2 legs of one right triangle are congruent to the corresponding parts of a 2nd triangle, then the triangles are congruent |
| State the Contrapositive of ITT | If 2 angles of a triangle are not congruent, then the sides opposite those angles are not congruent and the longer side is opposite the larger angle |
| State the Inverse of ITT | If 2 sides of a triangle are not congruent, then the angles opposite those sides are not congruent and the larger angle is opposite the longer side |
| State the 1st Minimum Theorem | The shortest segment from a point to a line is the perpendicular segment |
| State the Triangle Inequality Theorem | The sum of the lengths of any 2 sides of a triangle must be greater than the length of the 3rd side |
| State the Hinge Theorem | If 2 sides of 1 triangle are congruent to the corresponding parts of a 2nd triangle and the included angle of tehe 1st triangle is greater than the included angle of the second triangle, then the 3rd side of the 1st triangle is greater than the 3rd side of tehe 2nd triangle |
| State the Converse of the Hinge Theorem | If 2 sides of 1 triangle are congruent to the corresponding parts of a 2nd triangle and the 3rd side of the 1st triangle is greater than the 3rd side of the 2nd triangle, then the included angle of the 1st triangle is greater than the included angle of the 2nd triangle |
| The perpendicular segment from a vertex of the triangle to the line containing the opposite side is the ? | altitude |
| The median, angle bisector, and altitude of a triangle are distinct segments except in an isosceles triangle when they are ? | the same segment |
| The length of the altitude of any angle of a triangle is ? the lengths of at least 2 sides of the triangle | less than or equal to |
| The altitudes to the congruent sides of an isosceles triangle are ? | congruent |
| If 2 altitudes of a triangle are congruent, then the triangle is ? | isosceles |
| The altitude to the base of an isosceles triangle is also a ? | median |
| The altitudes of a(n) ? triangle are congruent | equilateral |
| The perimeter of a triangle is ? than the sum of the 3 altitudes | greater than |
| Given an altitude, an angle bisector, and a median, the altitude is the ? and the median is the ? of these 3 segments | shortest / longest |
| A theorem that states whether or not 2 sets intersect and if they intersect what the intersection looks like is called a ? theorem | incidence |
| This type of theorem shows at least 1 | existence |
| This type of theorem shows at most 1 | uniqueness |
| This type of theorem shows exactly 1 | existence and uniqueness |
| A theorem that states a condition that is satisfied by every point in a set, but none outside of the set is called a ? theorem | characterization |
| A line perpendicular to a segment at its midpoint is called a ? | perpendicular bisector |
| In a given plane, through a given point of a given line, there is ? line perpendicular to the given line | exactly 1 |
| State the Perpendicular Bisector Theorem | In a plane, the perpendicular bisector of a segment is the set of all points in the plane equidistant from the endpoints of the segment |
| In a plane, if 2 points of a line are each equidistant from the endpoints of a segment, then the line is the ? of the segment | perpendicular bisector |
| Through a given external point there is ? line perpendicular to a given line | exactly 1 |
| No triangle has more than one ? | right angle |
| The longest side (side opposite the right angle) of a right triangle is the ? | hypotenuse |
| A set of points used to make a proof easier is called a(n) ? | auxiliary set |
| If A-M-B on line L, then A and M are on the ? of any other line that contains B | same side |
| If A-M-B on line L and C is a point not on L then M is in the ? of angle ACB | interior |
| State the Crossbar Theorem | If M is in the interior of angle ACB then ray CM intersects segment AB |
| If A-M-C on line L then A and C are on ? of any other line that contains M | opposite sides |
| State the GH1 postulate | If A and E are on the same side of line BD and H and E are on the same side of line BD then A and H are on the same side of line BD |
| "If P then Q" is the ? | conditional |
| "If Q then P" is the ? | converse |
| "If not P then not Q" is the ? | inverse |
| "If not Q then not P" is the ? | contrapositive |
| Conditional and Contrapositive always have the same ? | truth value |
| Converse and Inverse always have the same ? | truth value |
| A statement that uses the words "if and only if" is a ? statement | biconditional |
| An isosceles triangle has ? sides congruent | at least 2 |
| An equilateral triangle has ? sides congruent | 3 |
| A scalene triangle has ? congruent sides | 0 |
| An equiangular triangle has ? congruent angles | 3 |
| A theorem that is the immediate consequence of another theorem is a ? | corrollary |
| State the Isosceles Triangle Theorem | If 2 sides of a triangle are congruent,then the angles opposite them are congruent |
| State the Converse of the Isosceles Triangle Theorem | If 2 angle of a triangle are congruent, then the sides opposite those angles are congruent |
| The bisector of the angle opposite the base of an isosceles triangle ? the base and is ? the base | bisects / perpendicular to |
| A line segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side is called a ? | median |
| the point of concurrency for medians is called the ? | centroid |
| the centroid is ? the way from the vertex to the opposite side | 2/3 |
| A line segment that lies on the bisector of the angle and has its endpoints as a vertex of the triangle and some point on the opposite side is called the ? | angle bisector of a triangle |
| the point of concurrency for angle bisectors is called the ? | incenter |
| a closed 4 sided figure is called a ? | quadrilateral |
| A quadrilateral with 4 right angles is called a ? | rectangle |
| a rectangle with 4 congruent sides is called a ? | square |
| the segment that joins 2 non-consecutive vertices of a quadrilateral is called the ? | diagonal |
| the median to the base of an isosceles triangle is ? the base and ? the angle opposite the base | perpendicular to / bisects |
| the medians to the congruent sides of an isosceles triangle are ? | congruent |
| Given 2 congruent triangles, the median to a side of 1 triangle is ? to the median to the corresponding side of the other triangle | congruent |
| the median to the base of an isosceles triangle ? the vertex angle | bisects |
| If a segment is perpendicular to one side of a triangle and also bisects the angle opposite that side, then the triangle is ? | isosceles |
| the point of concurrency for altitudes is called the ? | orthocenter |
