Geometry Honors Semester 1 Examination Check-List Study Guide

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Geometry

Honors Semester 1 Examination
Check
-
List
Study Guide

(
NOT

an exhaustive list of topics
)


Chapter 1


Recognize
points, lines, segments, rays, angles, and triangles


Identify the u
nion and intersection

of points, lines, segments, rays, angles, and

triangles


Measure

segments and angles


Classify angles


Name p
arts of a degree: converting from degrees to minutes and seconds, and vice versa


Recognize congruent angles and segments


Recognize collinear and noncollinear points (collinearity of poi
nts)


Recognize when a point is between two other points (the concept of betweenness)


Know what can be assumed from diagrams


Apply the t
riangle
-
inequality

principle


Identify m
idpoints

of segments


Identify
bisectors

and

trisectors

of segments and a
ngles


Write simple two
-
column proofs and p
aragraph proofs


Recognize the d
eductive structure

of geometry
: postulates, definitions, and theorems


Understand the characteristics and application of theorems


Recognize conditional statements and the

negat
ion,
the
converse,
the
inverse, and

the

contrapositive

of a
statement


Use the chain rule to draw conclusions


Solve p
robability

problems


Chapter 2


Understand the concept of
perpendicularity


Recognize c
omplementary and supplementary angles


Apply t
he five
-
step procedure to draw logical conclusions


Prove angles congurent by means of four

theorems in section 2.4 (c
ongruent supplements and complements
)


A
pply the a
ddition, subtraction, multiplication, and division properties

of segments and angles

(
know when
and
how
to use them)


Apply the t
ransitive and substitution properties

of angles and segments


Recognize opposite rays and v
ertical angles


Chapter 3


Understand the concept of c
ongruent figures


Accurately identify the corresponding parts of

figures


Identify included angles and included sides


Apply the SSS, SAS, and ASA postulates


Apply the principle of CPCTC (Congruent Parts of Congruent Triangles are Congruent)


Recognize some basic properties of circles


Apply the formulas for the
area and the circumference of a circle


Identify medians of triangles


Identify altitudes of triangles


Understand why auxiliary lines are used in some proofs


Write proofs involving steps beyond CPCTC


Use overlapping triangles in proofs


Name the v
arious types of triangles and their parts


Apply theorems relating the angle measures and side lengths of triangles


Use the HL postulate to prove
right

triangles congruent


Angle
-
side theorems


Ways to prove that a triangle is isosceles


Triangle Ine
qualities T
heorems

Chapter 4


Use d
etour
s in
proofs


Apply t
he midpoint formula


Organize the information in, and draw diagrams for, proof problems presented in words


A
pply one way of proving that two angles are right angles

(the R
ight
-
A
ngle
T
heorem
)


Recognize the relationship between equidistance and perpendicular bisection (t
he
Equidistance T
heorems
)


Recognize planes and transversals


Identify the pairs of angles formed by a transversal

(alt. ext., alt. int., corresp., same side ext, same side i
nt)


Recognize p
arallel lines and transversals


Understand the concept of sl
ope


Relate the slope of a line to its orientation in the coordinate plane (positive, negative, zero slope, undefined slope)


Recognize the relationships between the slopes

of
parallel and perpendicular lines


Chapter 5


Write i
ndirect proof
s

(proof by contradiction)


Apply various methods to p
rov
e

lines parallel


Apply the Exterior Angle Inequality T
heorem


Apply t
he
P
arallel
P
ostulate


Identify the pairs of a
ngles formed
when parallel lines are cut by a transversal


Apply six theorems about parallel lines


Solve crook problems


Know everything about
polygons


Identify special types of quadrilaterals and their properties


Proving that a quadrilateral is a parallelogram


Proving that figures are special quadrilaterals (rectangle, rhombus, square, kite, and isosceles trapezoid)


Chapter 6


Understand basic concepts relating to planes


Identify four methods of determining a plane


Apply two postulates concerning lines
and planes


Recognize when a line is perpendicular to a plane


Apply the basic theorem concerning the perpendicularity of a line and a plane


Recognize lines parallel to planes, parallel plans, and skew lines


Use properties relating parallel lines and

planes


Chapter 7


The sum of the measures of the three angles of a triangle


Definition
and the measure
of an exterior angle


Apply t
he No
-
Choice Theorem (know that the triangles do not have to be congruent)


Apply theorems about the interior angles,

the exterior angles, and the midlines of triangles


Apply
t
he AAS theorem


Use some important formulas that apply to polygons

(the sum of the measures of the interior angles of a polygon,
the sum of the measures of the exterior angles of a polygon, and
the number of diagonals that can be drawn in a
polygon)


Recognize regular polygons

(know their special names as well)


Use

a formula to find the measure of an exterior angle of an equiangular polygon