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Study Guide for Chapter 1 Test
Geometry
Please be aware that all tests are cumulative. Thus, anything that is required knowledge for
this first test may also appear on any future tests.
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In order to construct an object, use ONLY the compass and straightedge.
In order to draw an object, use tools that measure, such as the ruler and protractor.
In order to sketch an object, use no tools. Just move the pencil freehanded.
There are three undefined terms in Geometry: points, lines, and planes.
The three undefined terms can be described:
o A point has no size, although it does have location.
o A line consists of infinitely many points in a straight arrangement. A line has no
width, but it is infinitely long.
o A plane has length and width but no thickness.
The set of all points is called space.
Collinear points lie in the same line; coplanar points lie in the same plane.
Be able to name basic geometric objects using correct geometric symbolism. (See Notes 1.1)
To sketch a horizontal plane, sketch a parallelogram with two sides being horizontal.
To sketch a vertical plane, sketch a parallelogram with two sides being vertical.
Horizontal planes never intersect! (Example: The floor and ceiling in our room never intersect.)
Parallel planes, not necessarily horizontal, never intersect. (Example: The front and the back of our
classroom represent parallel planes that never intersect, yet they are not horizontal.)
Two or more vertical planes may intersect to form a line. (Example: Front and side of room.)
Any two planes that intersect form a line. (Example: Look where the front wall of the room meets the
side wall of the room. Or, look where the ceiling meets the front wall.)
Three planes may intersect to form a line. (Example: Stand a thin book on edge. The pages represent
many vertical planes intersecting in the binding that represents a line.)
Three planes may intersect to form a point. (Example: Look at a corner of the room.)
A ray consists of a point on a line and all of the points on that line that lie on one side of the
point.
Opposite rays lie on the same line in opposite directions, sharing a common endpoint.
The midpoint of a segment is the point that divides the segment into two congruent segments.
The bisector of a segment is a line, ray, segment, or plane that divides the segment into two
congruent segments.
Perpendicular lines are two lines that intersect to form right angles.
The perpendicular bisector of a segment is a line that divides a segment into two congruent
segments and is perpendicular to that segment.
Two adjacent angles lie in the same plane, have a common vertex, share a common side, and
do not overlap.
By definition, two objects are congruent if they are the same shape and size.
Definition: Congruent segments are segments that have equal lengths.
Definition: Congruent angles are angles that have equal measures.
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Note for future chapters… The above two definitions are very commonly used definitions in proofs.
So, in a proof, we may write as a reason “Definition of Congruent Segments” (abbreviated as “Def. of
 Segments”) or “Definition of Congruent Angles” (abbreviated as “Def. of  ' s ”).
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Complementary angles are two angles whose measures have a sum of 90  .
Supplementary angles are two angles whose measures have a sum of 180  .
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Be able to read and use other correct geometric symbolism:
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AB is read as “the distance from point A to point B”
AB  CD means that two lengths are the same. It is read as “the distance from point A to point B is
equal to the distance from point C to point D”.
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AB  CD means that two segments are congruent. It is read as “segment AB is congruent to
segment CD”.
m ABC  m DEF means that two angles have equal measures. It is read as “the measure of
angle ABC is equal to the measure of angle DEF”.
ABC  DEF means that two angles are congruent. It is read as “angle ABC is congruent to
angle DEF”.
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AB  CD means two segments are perpendicular. It is read as “segment AB is perpendicular to
segment CD”.
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Note: You can NEVER write
never congruent.
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Note: Only objects can be congruent. For example, it is correct to state AB  CD (because
segments are objects and objects can be congruent), but it is NOT correct to state AB  CD (because
distances are not objects).
AB  CD because lines can NOT be congruent. Likewise, rays are
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Be able to sketch geometric diagrams.
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When looking at a sketch, you ARE allowed to assume:
o points are collinear if they appear to lie on the same line.
o points are coplanar if they appear to lie within the parallelogram representing the plane.
o a line is contained within a plane if the entire line, including arrowheads, is sketched within the
parallelogram representing the plane.
o a line passes through a plane if part of the line is dashed, making it appear as if a portion is not visible
due to the plane blocking its view, and the arrowheads of the line are NOT sketched on the
parallelogram representing the plane. (If you are the one sketching a line intersecting a plane in
exactly one point, you should clearly mark the point of intersection between the line and the plane.)
o an angle is a straight angle if it appears to be one.
o angles are adjacent angles if they appear to be so.
o angles that appear to be vertical angles are congruent.
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When looking at a sketch, you are NOT allowed to assume:
o two lines are perpendicular – UNLESS they are marked with a perpendicular symbol (which appears to
form a small square at the intersection when sketched).
o an angle that appears to be a right angle is a right angle - UNLESS it is marked with a right angle
symbol (which appears to form a small square at the vertex when sketched).
o segments are congruent – UNLESS they are marked with congruency symbols (which look like the
same number of tic marks sketched perpendicularly across the segments).
o angles are congruent – UNLESS they are marked with congruency symbols (which look like the same
number of arc marks sketched in the interiors of the angles).
 Note: Vertical angles are the exception to this rule. You may assume they are congruent.
o lines are congruent. (Lines are NEVER congruent.)
o rays are congruent. (Rays are NEVER congruent.)
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Be able to do any of the constructions on the worksheet Introduction to Basic Constructions.
Be able to construct a regular hexagon by constructing a 6-point daisy first.
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A proof is logical, step-by-step, convincing argument.
Basic assumptions that are accepted without proof are called postulates.
Theorems are statements that are proved.
Informally, the Segment Addition Postulate states that if you add the lengths of two shorter
adjacent segments, you will get the total length.
Formally… Segment Addition Postulate: If we are given AB and BC on a line (where
point B is between A and C), then AB + BC = AC.
The word “equidistant” means “equal distance”.
Patty paper can be used to visually see that… a point that is equidistant to the two endpoints
of a segment MAY lie on the midpoint of that segment, but it MUST lie on the perpendicular
bisector of that segment.
Inductive Reasoning uses many observations to reach a conclusion. (Inductive Reasoning does
NOT prove something is true. A counterexample simply may not have been discovered yet.)
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An angle is a figure formed by two rays that have the same endpoint. The two rays are called
the sides of the angle, and their common endpoint is the vertex of the angle.
o An acute angle has a measure between 0 and 90 degrees.
o A right angle has a measure of exactly 90 degrees.
o An obtuse angle has a measure between 90 and 180 degrees.
o A straight angle has a measure of exactly 180 degrees.
The size of an angle is determined by the measure of the angle. You could use a protractor to
measure the size of an angle. The length of the rays that are sketched or drawn to represent
the sides of the angle does NOT determine the size of the angle.
An angle bisector is a ray that divides the angle into two congruent angles.
Informally, the Angle Addition Postulate states that if you add the measures of two smaller
adjacent angles, you will get the total measure.
Formally… Angle Addition Postulate: If we are given that point B lies in the interior of
AOC , then m AOB  m BOC  m AOC .
Informally, vertical angles are formed directly across from each other by two intersecting
lines.
Vertical angles are always congruent.
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x x y y 
Midpoint Formula: midpoint   1 2 , 1 2 
2 
 2
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Distance Formula:
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Be able to use the Midpoint Formula and Distance Formula. (See Notes and HW for 1.3)
Be able to simplify radicals.
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Know the difference between convex and concave polygons.
Know the names of polygons, from triangle (3 sides) to dodecagaon (12 sides). (See Notes 1.4)
Be able to find the perimeter and area of triangles, squares, and rectangles. Formulas - p.31.
d
 x2  x1    y2  y1 
2
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(See Notes and Assignment 1.4)
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Be able to find the measure of angles – using geometry to write an equation and showing all
algebraic steps to solve the equation. (See Notes and Assignment 1.5 & Assignment 1.6)