Geometry Review 1 st Quarter

1. Geometry Review1st Quarter Definitions Theorems 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.

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.

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. The end. • Good luck on the test!