Geometry Study Guides
by Julie Stalling
What you learn is more important than your grade!
Click on one of the following chapters to review what you have learned.
Your textbook supplies a never ending number of web sites to visit as you learn more about geometry! Just click here and begin an adventure of discovery!
Chapter 1 Introduction to Geometry
When you prepare for
your first test, be sure to review the following topics:
~ Dictionary (including the terms, definitions and pictures)
~ Measure segments and angles
~ Sketch and label a picture
~ Word problems like section 1.7
~ True/false statements
The following
statements are ALL TRUE.
(Please forgive me for the spacing and geometric
symbols that don't get converted right when put into web
language.)
1. For every line segment there is exactly one midpoint.
- For every angle there is exactly one angle bisector.
- If two different lines intersect, then they intersect at one and only one point.
- If two different circles intersect, then they intersect at one, or two points or an infinite number of points.
- Through a given point on a line there is an infinite number of lines perpendicular to the given line.
- In every triangle there cannot be more than one right angle.
- Through a point not on a line, one and only one line can be constructed parallel to the given line.
- If CA = AT, then A may be the midpoint of CT.
- If m(angle)D = 40° and m(angle)C = 140°, then angles C and D are a supplementary pair.
- If point A is not the midpoint of CT, then CA might not be equal to AT, but it is possible.
- An acute angle is an angle whose measure is less than 90°.
- If two lines intersect to form a right angle, then the lines are perpendicular.
- A diagonal is a line segment that connects any two nonconsecutive vertices of a polygon.
- A ray that divides the angle into two congruent angles is the angle bisector.
- An obtuse triangle has exactly one angle whose measure is greater than 90°.
16. Only one plane can pass through three noncollinear points.
- If a line intersects a plane that does not contain the line, then the intersection is exactly one point.
- If two lines are perpendicular to the same line, then they may or may not be parallel.
- If two different planes intersect, then their intersection is a line.
- If a line and a plane have no points in common, then they are parallel.
- If a plane intersects two parallel planes, then the lines of intersection are parallel.
- If three random planes intersect (no two are parallel and all three do not share the same line), then they divide space into seven parts.
- If two lines are perpendicular to the same plane, then they are parallel to each other.
- The three basic building blocks of geometry are point, line and plane.
- The ray through point Q from point P is written in symbolic form at PQ (with an arrow of the top and pointing to the right).
- The length of segment PQ can be written as PQ (with a segment over the top).
- The vertex of angle PDQ is point D.
- The symbol for perpendicular is an upside down T.
- A scalene triangle is a triangle with no two sides the same length.
- An acute angle is an angle whose measure is less than 90°.
- If AB intersects CD at point P, then (angle)APD and (angle)APC are a pair of linear angles.
- If two lines lie in the same plane and are perpendicular to the same line, then they are parallel.
- If the sum of the measure of two angles is 180°, then the two angles are supplementary.
- A trapezoid is a quadrilateral having exactly one pair of parallel sides.
- A polygon with ten sides is a decagon.
- A square is a rectangle with all the sides equal in length.
- A pentagon has five sides and five diagonals.
- The largest chord of circle is a diameter of the circle.
Chapter 2-3-4 Angle Relationships
Multiple choice interactive review for angles created by parallel lines cut by a transversal.
When you prepare for
your angle relationships test, be sure to review the following
topics:
~ Eight conjectures
~ Four definitions
~ Five special pairs of angles
~ Triangle sum
~ Isosceles triangles
~ Solve for a missing angle measure
~ Construct congruent segments
~ Construct congruent angles
~ Construct parallel lines in three ways
Chapter 4-11 Congruence and Similarity
Multiple choice interactive
review for isosceles and equilateral triangles.
Multiple choice interactive
review for polygon properties.
Multiple choice interactive
review for similar polygons.
When you prepare for
your congruence and similarty test, be sure to review the following
topics:
~ Congruent triangles with SSS, SAS, ASA, SAA
~ CPCTC sentences
~ Flowcharts
~ Construct an angle bisector
~ Isosceles triangle properties
~ Solve proportions
~ Solve similar polygons and triangles
Return to table
of contents
These constructions will not be on a test until the
midterm.
~ Midpoint of a segment
~ Perpendicular bisector of a line from the point on the line
~ Perpendicular bisector of a line from a point not on the line
Multiple choice interactive review for parallelogram properties.
When you prepare for
your polygon test, be sure to review the following
topics:
~ Interior and exterior angles of a polygon
~ Four kite conjectures
~ Three trapezoid conjectures
~ Midsegment of a triangle
~ Midsegment of a trapezoid
~ Properties of parallelograms and special parallelograms
When you prepare for
your midterm test, be sure to review the following
topics:
~ Chapter one dictionary
~ Special pairs of angles
~ Congruent triangles
~ Similar triangles
~ Polygon properties
~ All of our constructions
Remember that working on your web poster is reviewing for your
midterm test!
Multiple choice interactive review for circles.
When you prepare for
your circles test, be sure to review the following
topics:
~ Chord properties
~ Tangent properties
~ Pi
~ Circumference
~ Arc length
Multiple choice interactive review for area.
When you prepare for
your area test, be sure to review the following topics:
~ Calculate area for rectangles, parallelograms, triangles,
trapezoids, kites, regular polygons, sectors, segments, and
annulus.
~ Find a missing value when given an area
~ Apply area formulas to "real-life"
When you prepare for
your right triangles test, be sure to review the following
topics:
~ Simplify square roots
~ Solve right triangles with the Pythagorean Theorem
~ Solve 45-45-90 and 30-60-90 triangles
~ Solve the distance formula
~ Solve for right triangles in a circle
~ Apply the Pythagorean Theorem to "real-life"
When you prepare for
your volume test, be sure to review the following
topics:
~ Study dictionary terms
~ Calculate volume for prisms, cylinders, pyramids, cones and
spheres
~ Calculate volume of irregular shaped solids with water
displacement
~ Apply volume formulas to "real-life"
Chapter 12 Introduction to Trigonometry
When you prepare for
your trigonometry test, be sure to review the following
topics:
~ Read and trigonometry table of values
~ Solve right triangles using SOHCAHTOA
~ Solve triangles using the law of sines or the law of cosines
~ Apply trigonometry to "real-life"
