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Geometry
Segment 1 EXAM STUDY GUIDE
 Vocabulary (Module 1):
o Undefined terms of Geometry: point, plane, line
 Identify points by a single, capital letter
 Identify lines by a cursive lowercase letter or by two points on the line
 Identify planes by either a capital, italicized letter or three points on the plane
o Coplanar – points that lie in the same plane
o Ray
o Intersection (as a point, line, or plane)
o Collinear – points that lie in the same line
o Segment
o Measure of an angle – m < A is read “measure of angle A”
o Midpoint of a segment – the midpoint splits a segment into two congruent parts
o Vertex of an angle – the point in the middle of an angle
o Acute, Right, Obtuse, and Straight angles
o Linear Pair – two angles that form a straight angle (180 degrees)
o Adjacent angles
o Complementary angles – angles that add up to 90 degrees
o Supplementary angles – angles that add up to 180 degrees
o Vertical angles
o Compass, protractor, straight edge – tools used for Geometry constructions
 Concepts from Module 1:
o Finding the length of a segment (1.04)
o Finding the distance between two points (1.05)
 Distance formula: ( x2  x1 )2  ( y2  y1 )2 given two points (x1, y1) and (x2, y2)
o Finding the midpoint between two points (1.05, 1.12)
x x y y 
 Midpoint formula:  1 2 , 1 2  given two points (x1, y1) and (x2, y2)
2 
 2
o Finding the measure of an angle given the degree measures or expression of other
angles (1.08)
 Vocabulary (Module 2):
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Parallel, perpendicular, skew, intersect
Transversal
Corresponding Angles – congruent in parallel lines
Alternate Interior or Exterior Angles – congruent in parallel lines
Same-side interior or exterior angles – supplementary in parallel lines
Conditional statements, converse statements, inverse statements, contrapositive
statements, biconditional statements (2.07)
o Hypothesis and conclusion
o Algebraic Properties – please see 2.08 for a complete list with definitions
o Horizon line, vanishing point, convergence lines, perspective lines
 Concepts from Module 2:
o Slope: Given two points on a line, use the slope formula to find the slope: (y2 – y1) / (x2 –
x1)
 Find the slope of (8, -2) and (-2, 1):
(1 - -2) / (-2 – 8) = 3/-10
o Parallel lines have THE SAME SLOPE
 If a line has a slope of ¾, a parallel line also has a slope of ¾
o Perpendicular lines have OPPOSITE RECIPROCAL slopes
 If a line has a slope of ¾, a perpendicular line then has a slope of -4/3
o Using Algebraic Properties to justify statements in a proof (2.08 and 2.09)
 Vocabulary (Module 3):
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Equilateral Triangles – all sides congruent, all angles equal to 60 degrees
Isosceles triangles – two sides congruent, two base angles congruent
Scalene triangles – no sides congruent, no angles congruent
Equiangular Triangle – three congruent angles
Acute triangle – all angle less than 90 degrees
Right triangle – one angle that is 90 degrees and two acute
Obtuse triangle – one angle greater than 90 degrees and two acute
Triangle Sum Theorem – the sum of the measures of the angles in a triangle equals 180
degrees
Triangle Exterior Angle Theorem – the measure of each exterior angle is the sum of the
measure of its two remote interior angles
Isosceles Triangle Theorem – if two sides of a triangle are congruent, then the angles
opposite those sides are congruent
Triangle Inequality Theorem – The sum of the lengths of any two sides of a triangle is
greater than the third side and
Congruency Postulates – see 3.07 for a complete list with definitions – SSS, SAS, ASA,
AAS; see 3.11 for right triangle congruency postulates – HL, LL
CPCTC – once you’ve proven two triangles are congruent, you can use CPCTC to say
that two parts of the congruent triangle are also congruent
 Concepts from Module 3:
o Find a missing angle given the exterior angle or the two remote interior angles (3.03)
o Angle Puzzler (3.04)
o Find the missing angle given the exterior angle, base angle, or vertex angle of an
isosceles triangle (3.05)
o Finding the possible third side of a triangle given two sides (3.06)
o Shortest side of a triangle is opposite the smallest angle, longest side of a triangle is
opposite the largest angle (3.06)
 Vocabulary (Module 4):
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Median – middle of a segment
Perpendicular Bisector
Angle Bisector
Altitude
Midsegment
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Incenter – intersection of the angle bisectors
Circumcenter – intersection of the perpendicular bisectors
Centroid –
Geometric Means and extremes
Scale factors
Sine, cosine, tangent
Cosecant, secant, cotangent
 Concepts from Module 4:
o Setting up proportions to find certain sides or angles of a triangle (4.08)
o Applying Pythagorean Theorem (4.09)
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If c2 > a2 + b2, then the triangle is obtuse
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If c2 < a2 + b2, then the triangle is acute
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If c2 = a2 + b2, then the triangle is right
o Special Right Triangles (4.10)
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45-45-90: both legs are congruent and the length of the hypotenuse is 2
times the length of a leg.
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30-60-90: the length of the hypotenuse is twice the length of the shorter leg.
The length of the longer leg is 3 times the length of the shorter leg
o Trigonometric Ratios SOH CAH TOA (4.11):
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Sine = opposite/hypotenuse
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Cosine = adjacent/hypotenuse
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Tangent = opposite/adjacent
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Cosecant = hypotenuse/opposite
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Secant = hypotenuse/adjacent
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Cotangent = adjacent/opposite
o Inverse sine, cosine, tangent – use this to help you find the degree of the desired angle
(4.11).