1. Geometry Review 1 st Quarter Definitions Theorems Parts of Proofs Parts of Proofs

2. Definitions  Another name for an if-then statement is  a conditional.  Every conditional has two parts. The part following the if is the  hypothesis, and the part following the then is the  conclusion.  When you determine whether a conditional is true or false, you determine its  truth value.

3.  If you interchange the hypothesis and the conclusion of a conditional you get the  converse.  When a conditional and its converse are true, you can combine them as a  biconditional.  The negation of a statement has the  opposite meaning.  If you negate both the hypothesis and the conclusion of a conditional you get the  inverse.

4.  If you interchange and negate the hypothesis and conclusion of a conditional you get the  contrapositive.  If two angles are complementary, then  The sum of their measures is 90.  If two angles are supplementary, then  The sum of their measures is 180.  If the sides of two angles form a pair of opposite rays, then  The angles are vertical angles.

5.  The segment connecting the midpoints of two sides of a triangle is the  midsegment.  A postulate is a statement that is  assumed to be true.  A set of points that meets a stated condition is known as  a locus.  A theorem is a statement that is  proven.

6.  When two statements have the same truth value we say that they are  logically equivalent.  The set of points common to two figures is the  Intersection of the figures.  Two objects that have the same size and shape are said to be  Congruent.  Back to title page. Back to title page. Back to title page.

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

8.  All right angles are  congruent.  If two angles are congruent and supplementary, then each  is a right angle.  If a segment joins the midpoints of two sides of a triangle, then the segment is  parallel to the third side and half its length.  The sum of the lengths of any two sides of a triangle is  greater than the length of the third side.

9.  If two sides of a triangle are not congruent, then the larger angle  lies opposite the longer side.  If two angles of a triangle are not congruent, then the longer side  lies opposite the larger angle.  If a point is on the perpendicular bisector of a segment, then it is  equidistant from the endpoints.  If a point is equidistant from the endpoints of a segment, then it is on the  perpendicular bisector of the segment.

10.  If a point is on the bisector of an angle, then it is  equidistant from the sides of the angle.  If a point in the interior of an angle is equidistant from the sides of the angle, then  it is on the angle bisector.  If the exterior sides of two adjacent acute angles are perpendicular, then  the angles are complementary.  Through a point outside a line,  1) there is only one line perpendicular to the given line.  2) there is only one line parallel to the given line.  Back to title page. Back to title page. Back to title page.

11. Parts of Proofs  A proof in two-column form has 5 parts:  1. A diagram or figure showing the given information.  2. A list of the given information.  3. A list of what is to be proved.  4. A logical series of statements.  5. The reasons why each statement is true.

12. TTTThe end.  G G G Good luck on the test!