Please enable JavaScript.
Coggle requires JavaScript to display documents.
Geometry Exam One Review - Coggle Diagram
Geometry Exam One Review
Chapter One
-
Section 1-3 - Postulate 1-3: If two planes intersect, then they intersect in exactly one line.
-
Section 1-2 - You can create an orthographic drawing by showing the top view, front view, and right-side view of a three-dimensional figure.
-
Section 1-4 - A segment is the part of a line consisting of two endpoints and all points between them.
A ray is the part of a line consisting of one endpoint and all the points of the line on one side of the endpoint.
-
Section 1-2 - You can create an isometric drawing on isometric dot paper to show three sides of a figure from a corner view.
-
Section 1-5 - Ruler Postulate: The points of a line can be put into one-to-one correspondence with the real numbers so that the distance between any two points is the absolute value of the difference of the corresponding numbers.
Segment Addition Postulate: If three points A, B, and C are collinear and B is between A and C, then AB+BC=AC.
-
Section 1-6 - An angle is formed by two rays with the same endpoint. The rays are the sides of the angle and the endpoint is the vertex of the angle.
The measure of acute angles is between 0 and 90 degrees, the measure of right angles is 90 degrees, the measure of obtuse angles is between 90 degrees and 180 degrees, and the measure of straight angles is 180 degrees.
Protractor Postulate: Let ray OA and ray OB be opposite rays in a plane. Ray OA, ray OB, and all the rays with endpoint O that can be drawn on one side of segment AB can be paired with the real numbers from 0 to 180 so that ray OA is paired with 0 and ray OB is paired with 180. If ray OC is paired with x and ray OD is paired with y, then the measure of angle COD is the absolute value of x-y.
Angle Addition Postulate: If point B is in the interior of angle AOC, then the measure of angle AOB plus the measure of angle BOC is the measure of angle AOC.
-
Section 1-7 - In a construction, you use a straightedge and a compass to draw a geometric figure. A straightedge is a ruler with no markings and a compass is a geometric tool used to draw circles and arcs.
Perpendicular lines are two lines that intersect to form right angles. A perpendicular bisector of a segment is a line, segment, or ray that is perpendicular to the segment at its midpoint, thereby bisecting the segment into two congruent segments.
Section 1-8 - In coordinate geometry, you describe a point by an ordered pair (x, y), called the coordinates of the point.
To find the coordinate of the midpoint of a segment on a number line, you need to find the average or mean of the coordinates of the endpoints.
Section 1-9 - The perimeter of a polygon is the sum of the lengths of its sides. The area of a polygon is the number of square units it encloses.
Postulate 1-9: If two figures are congruent, then their areas are equal.
-
Chapter Three
-
Section 3-2 - The converses of the Corresponding Angles Postulate, Alternate Interior Angles Theorem, Same-Side Interior Angles Theorem, Alternate Exterior Angles Theorem, and Same-Side Exterior Angles Theorem are all true postulates and theorems.
A flow proof is a proof in which arrows show the logical connections between statements and reasons are written below the statements.
Section 3-3 - Theorem 3-9: If two lines are parallel to the same line, then they are parallel to each other.
Theorem 3-10: In a plane, if two planes are perpendicular to the same line, then they are parallel to each other.
-
Theorem 3-11: In a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other.
Section 3-4 - Triangle Angle-Sum Theorem: The sum of the measures of the angles of a triangle is 180.
An equiangular triangle is a triangle in which all angles are congruent. An equilateral triangle is a triangle in which all sides are congruent. An isosceles triangle is a triangle in which at least two sides are congruent. A scalene triangle is a triangle in which no sides are congruent.
Triangle Exterior Angle Theorem: The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.
-
Section 3-5 - A polygon is a closed plane figure with at least three sides that are segments. The sides intersect only at their endpoints, and no adjacent sides are collinear.
-
Section 3-6 - The slope-intercept form of a linear equation is y=mx+b, where m is the slope of the line and b is the y-intercept.
The standard form of a linear equation is Ax+By=C, where A, B, and C are real numbers and A and B are not both zero.
The point-slope form for a nonvertical line through point (x₁, y₁) with slope m is y-y₁=m(x-x₁).
Section 3-7 - If two nonvertical lines are parallel, their slopes are equal. If the slopes of two distinct nonvertical lines are equal, the lines are parallel. Any two vertical lines are parallel.
If two nonvertical lines are perpendicular, the product of their slopes is -1. If the slopes of two lines have a product of -1, the lines are perpendicular. Any horizontal line and vertical line are perpendicular.
Section 3-8 - You can use what you know about parallel lines, transversals, and corresponding angles to construct parallel lines.
-
Chapter Two
Section 2-1 - A conditional is an if-then statement. The part following "if" is the hypothesis, while the part following "then" is the conclusion.
-
Section 2-2 - A biconditional is a statement that connects the conditional and its converse with the word "and". It can only be used when both the conditional and its converse are true.
A good geometric definition uses clearly understood terms, has precise language, and is reversible. A good way to demonstrate that a statement is not a good definition is by finding a counterexample.
Section 2-3 - Deductive reasoning is the process of logically reasoning from given statements to a conclusion. If the given statements are true, then deductive reasoning produces a true conclusion.
Law of Detachment: If a conditional is true, and its hypothesis is true, then its conclusion is true.
Law of Syllogism: If p-q and q-r are true statements, then p-r is a true statement.
-
-
Chapter Four
Section 4-1 - Congruent figures have the same size and shape. Congruent polygons have congruent corresponding parts - their matching sides and angles.
Theorem 4-1: If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent.
-
Section 4-2 - Side-Side-Side (SSS) Postulate: If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
Side-Angle-Side (SAS) Postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
-
Section 4-3 - Angle-Side-Angle (ASA) Postulate: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
Angle-Angle-Side (AAS) Theorem: If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles are congruent.
-
Section 4-4 - Once you have figured out that triangles are congruent, you can make conclusions about their other parts because, by definition, corresponding parts of congruent triangles are congruent. This is abbreviated as CPCTC.
Section 4-5 - The congruent sides of an isosceles triangle are its legs. The third side is its base. The two congruent sides form the vertex angle, while the other two angles are the base angles.
Isosceles Triangle Theorem: If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
-
Section 4-6 - In a right triangle, the side opposite the right angle is the longest side and is called the hypotenuse. The other two sides are called legs.
Hypotenuse-Leg (HL) Theorem: If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another triangle, then the triangles are congruent.
Section 4-7 - Overlapping triangles may have a common side or angle. You can simplify your work with overlapping triangles by separating and redrawing the triangles.
In overlapping triangles, a common side or angle is congruent to itself by the Reflexive Property of Congruence.
