Geometry ReviewGeometry Review11stst Quarter Quarter

DefinitionsDefinitions

Theorems Theorems

Parts of ProofsParts of Proofs

DefinitionsDefinitions

Another name for an Another name for an if-thenif-then statement is statement is a a conditionalconditional.. Every conditional has two parts. The part Every conditional has two parts. The part

following the following the ifif is the is the hypothesishypothesis, and the part following the , and the part following the thenthen is the is the conclusionconclusion.. When you determine whether a conditional is true When you determine whether a conditional is true

or false, you determine itsor false, you determine its truth valuetruth value..

If you interchange the hypothesis and the If you interchange the hypothesis and the conclusion of a conditional you get theconclusion of a conditional you get the

converseconverse.. When a conditional and its converse are When a conditional and its converse are

true, you can combine them as atrue, you can combine them as a biconditionalbiconditional.. The The negationnegation of a statement has the of a statement has the opposite meaning.opposite meaning. If you negate both the hypothesis and the If you negate both the hypothesis and the

conclusion of a conditional you get theconclusion of a conditional you get the inverseinverse..

If you interchange and negate the If you interchange and negate the hypothesis and conclusion of a conditional hypothesis and conclusion of a conditional you get theyou get the

contrapositivecontrapositive.. If two angles are complementary, thenIf two angles are complementary, then The sum of their measures is 90.The sum of their measures is 90. If two angles are supplementary, thenIf two angles are supplementary, then The sum of their measures is 180.The sum of their measures is 180. If the sides of two angles form a pair of If the sides of two angles form a pair of

opposite rays, thenopposite rays, then The angles are vertical angles.The angles are vertical angles.

The segment connecting the midpoints of The segment connecting the midpoints of two sides of a triangle is thetwo sides of a triangle is the

midsegmentmidsegment.. A postulate is a statement that isA postulate is a statement that is assumed to be true.assumed to be true. A set of points that meets a stated condition A set of points that meets a stated condition

is known asis known as a a locus.locus. A theorem is a statement that isA theorem is a statement that is proven.proven.

When two statements have the same truth When two statements have the same truth value we say that they arevalue we say that they are

logically equivalent.logically equivalent. The set of points common to two figures is The set of points common to two figures is

thethe Intersection of the figures.Intersection of the figures. Two objects that have the same size and Two objects that have the same size and

shape are said to beshape are said to be Congruent.Congruent. Back to title page.Back to title page.

TheoremsTheorems

Vertical angles areVertical angles are congruent.congruent. If two parallel lines are cut by a transversal, thenIf two parallel lines are cut by a transversal, then 1) alternate interior angles are congruent.1) alternate interior angles are congruent. 2) alternate exterior angles are congruent.2) alternate exterior angles are congruent. 3) same-side interior angles are supplementary.3) same-side interior angles are supplementary. In a plane, two lines perpendicular to the same line areIn a plane, two lines perpendicular to the same line are parallel to each other.parallel to each other. If two intersecting lines form congruent, adjacent angles, If two intersecting lines form congruent, adjacent angles,

thenthen the lines are perpendicular.the lines are perpendicular.

All right angles areAll right angles are congruent.congruent. If two angles are congruent and If two angles are congruent and

supplementary, then eachsupplementary, then each is a right angle.is a right angle. If a segment joins the midpoints of two sides If a segment joins the midpoints of two sides

of a triangle, then the segment isof a triangle, then the segment is parallel to the third side and half its length.parallel to the third side and half its length. The sum of the lengths of any two sides of a The sum of the lengths of any two sides of a

triangle istriangle is greater than the length of the third side.greater than the length of the third side.

If two sides of a triangle are not congruent, If two sides of a triangle are not congruent, then the larger anglethen the larger angle

lies opposite the longer side.lies opposite the longer side. If two angles of a triangle are not congruent, If two angles of a triangle are not congruent,

then the longer sidethen the longer side lies opposite the larger angle.lies opposite the larger angle. If a point is on the perpendicular bisector of If a point is on the perpendicular bisector of

a segment, then it isa segment, then it is equidistant from the endpoints.equidistant from the endpoints. If a point is equidistant from the endpoints of If a point is equidistant from the endpoints of

a segment, then it is on thea segment, then it is on the perpendicular bisector of the segment.perpendicular bisector of the segment.

If a point is on the bisector of an angle, then it isIf a point is on the bisector of an angle, then it is equidistant from the sides of the angle.equidistant from the sides of the angle. If a point in the interior of an angle is equidistant If a point in the interior of an angle is equidistant

from the sides of the angle, thenfrom the sides of the angle, then it is on the angle bisector.it is on the angle bisector. If the exterior sides of two adjacent acute angles If the exterior sides of two adjacent acute angles

are perpendicular, thenare perpendicular, then the angles are complementary.the angles are complementary. Through a point outside a line,Through a point outside a line, 1) there is only one line perpendicular to the given 1) there is only one line perpendicular to the given

line.line. 2) there is only one line parallel to the given line.2) there is only one line parallel to the given line. Back to title page.Back to title page.

Parts of ProofsParts of Proofs

A proof in two-column form has 5 parts:A proof in two-column form has 5 parts: 1. A 1. A diagramdiagram or or figurefigure showing the given showing the given

information.information. 2. A list of the 2. A list of the givengiven information. information. 3. A list of what is to be 3. A list of what is to be provedproved.. 4. A logical series of 4. A logical series of statementsstatements.. 5. The 5. The reasonsreasons why each statement is true. why each statement is true.

The end. The end. Good luck on Good luck on

the test!the test!