Pre-AP Geometry Semester Study Guide

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Oct 10, 2013 (3 years and 8 months ago)

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Pre
-
AP
Geometry Semester Study Guide


The following will give you an idea of the topics and vocabulary that you might see on
the semester exam. The attached problem set is intended to be a sample of the types of
problems you may see. It should not be you
r only source of review



use your book and
notes for other practice problems.


The test will be mostly multiple choice questions with a few

proofs

and/or written
responses
.


Chapter 1
: Foundations



Naming points, lines, rays, planes, segments, and their i
ntersections



Identifying types of angles and solving equations using them

o

Vertical angles

o

Linear pair angles

o

Supplementary angles

o

Complementary angles

o

Bisected angles

o

Adjacent angles



Use midpoint and distance formula


Chapter 2
: Reasoning



Write condition
al statements

o

Conditional

o

Converse

o

Inverse

o

Contrapositive

o

Biconditional



Determine whether conditionals are true or false & provide counterexamples if
false



Use justifications to support conclusions

o

Definitions

o

Postulates

o

Theorems

o

Properties



Other vocab
: truth value, inductive and deductive reasoning


Chapter 3: || &


Lines



Identify types of angles formed by 2 lines & a transversal

o

Alternate interior

o

Alternate exterior

o

Corresponding

o

Same side interior



Show when lines are parallel and solve equations us
ing the theorems of

s above



Find slopes of lines given two points, an equation of a line, or the graphed line



Identify if lines are parallel, perpendicular, intersecting, or coinciding by their
slopes



Other vocab: skew lines, point
-
slope and slope
-
interce
pt form of a linear equation


Chapter 4: Δ Congruence



Know and apply the Triangle sum theorem



Know and apply the Exterior angles theorem



Know and apply the 5 ways to prove two triangles congruent



Know what CPCTC stands for and how to apply it



Know and appl
y the Isosceles Triangle theorem



Write a proof using congruent triangles



Write a coordinate proof using variable coordinates


Chapter 5: Properties of Triangles



Identify and apply the theorems of segments of a triangle

o

Perpendicular bisector

o

Angle bisect
or

o

Median

o

Altitude

o

Midsegment



Know the apply the theorems related to centers of a triangle

o

Circumcenter

o

Incenter

o

Orthocenter

o

Centroid



Know and apply the Triangle Inequality theorem



Know and apply the Unequal Sides and Angles theorem



Know and apply the P
ythagorean theorem to find missing side & to determine if a
triangle is acute, right, or obtuse



Know and apply the Special Right Δ theorems


Chapter 7: Similarity



Use proportions to solve problems involving similar polygons



Know the 3 ways to prove 2 trian
gles are similar



Apply the Proportional Perimeters and Areas Theorem to similar polygons


Chapter 8: Right Triangles and Trigonometry



Apply geometric mean theorems to right triangles to solve for missing lengths


Chapter 12: Transformations



Identify and dr
aw reflections, rotations, & translations on the coordinate plane



Identify, draw, and describe compositions of transformations including glide
reflections and those resulting from reflecting over 2 parallel lines or reflecting
over 2 intersecting lines



Identify the type of symmetry a figure has

o

2D shapes



Line (state how many lines and where they are)



Rotational (state the order and degree of rotation)

o

3D shapes



Plane (state how many planes)



Axis (state the order and degree of rotation)

o

Frieze patterns an
d Tessellations



Translation



Reflection



Rotation



Glide reflection



Dilate a figure on the coordinate plane and apply properties of scale factor