Geometry A Unit 1-4

SMART : Specific Measurable Achievable Realistic Relevant Timely

Know how to make nets and drawings of three dimensional figures. : ...

Space : is the set of all points in three dimensions

Segment : a portion of a line that has two endpoints

Co planar :

Plane : is a flat surface that extends without end. It can be named by capital letter or three points in the plane not in a line.

Find and compare lengths of segments : ...

Segment bisector : means to divide, not just in two, but in halves, or two equal parts. Therefore, a segment bisector is a point, a line, a ray, or a line segment that bisects another line segment.

Find and compare the measures of angles : ...

Angle : is formed by two rays with the same end point

Acute Angle : Less than 90 degrees

Right Angle : Exactly 90 degrees

Protractor : is a tool used to measure angles

There are _________ methods for naming angles. : Three

Supplementary Angles : are two angles whose measures have a sum of 180. Each angle is called the supplement of the other.

Linear pair : is a pair of adjacent angles whose non-common sides are opposite rays. Form a straight angle.

congruent segments : identical in length to an existing segment

congruent angles : identical to another angle

Find the midpoint of a segmentFind the distance between two points in the coordinate plane : ...

Distance Coordinate Plane Formula :

Find the perimeter or circumference of basic shapesFind the area of basic shapes : ...

Square : Perimeter=4sArea= s×s

Conditional : an if-then statement Use hypothesis and conclusion. p=q If p then q

Hypothesis : The part p of a conditional statement following the word if

Inverse : Negate both the hypothesis and the conclusion of the conclusion of the conditional. -p=-qIf not p, then not q

Contrapositive : the statement formed by negating both the hypothesis and conclusion of the converse of a conditional statement-p = -qIf not q then not p

Detuctive Reasoning : is a method whereby conclusions follow from general principles

two-column proof : a type of proof written as numbered statements and reasons that show the logical order of an argument

Addition Property Subtraction PropertyMultiplication Property Division Property Distributive Property : ...

Writing proofs can be tricky. The more practice you have writing proofs, the easier it will become. The tips listed below may help you with the process of writing two-column proofs: : 1. Use logical thinking, and ask yourself questions such as these:What do I know (the facts)?What am I trying to prove?Does the given information or the diagram lead to other facts?For example, if it is given that a point is the midpoint of a line segment, then I know that the two segments on either side of the midpoint are congruent and equal in length.2. If the proof involves a diagram, mark all the given information on the diagram. This visual will help you make connections between what you are given and what you are trying to prove. It may also lead you to discover other information that can help you develop the proof.3. Remember, not all proofs will be exactly the same since the given information, prove statements, and diagrams will vary. Each proof must be addressed independently. Although there is no "formula" for writing a proof, the same process can be applied to each proof.4. There may be multiple variations for the same proof. For example, you and a classmate may not have the exact same statements and reasons for the same proof, but you both may be correct. 5. You may find it easier to outline a plan before you begin writing the two-column proof.6. Remember, you must always use facts for reasons, such as given information, properties, definitions, previously proved theorems, and postulates. Also, each statement must be supported with a reason.

Vertical Angles Theorem : If two angles are vertical angles, then they are congruent.

Congruent Complements Theorem : If two angles are complementary to the same angle (or to congruent angles), then they are congruent.All right angles are congruent. If two angles are congruent and supplementary then each is a right angle.

Transversal : a line that intersects two or more coplanar lines at two different points

Alternate exterior Angles : nonadjacent exterior angles that lie on opposite sides of the transversal

Corresponding Angles Postulate : If a transversal intersects two parallel lines, then corresponding angles are congruent.

Alternate Interior Angles Theorem : If a transversal intersects two parallel lines, then alternate interior angles are congruent.

Converse of the Alternate Interior Angles Theorem : If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel.

Converse of the Same-Side Interior Angles Theorem : If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel.

Perpendicular and Parallel Lines Theorem : In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

Perpendicular Transversal Theorem : In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.

Exterior angle of a polygon : an angle formed by a side and an extension of an adjacent side

remote interior angles : the angles of a triangle that are not adjacent to a given exterior angle

Construct parallel and perpendicular linesConstruct special quadrilaterals and a regular polygon inscribed in a circle : ...

Perpendicular Postulate : Through a point not on a line, there is one and only one line perpendicular to the given line.