4.1 Congruent Figures
-Congruent figures- figures with the same size and shape- if the angles of one polygon are
congruent to the angles of another polygon, and the sides of the two polygons are congruent, then
the polygons are congruent
-If you know two
11.1 Area of a Rectangle
-the area of a figure is the area of a region that the area encloses. An area is measured in
square units, which means squares whose sides are the basic unit of measure
Postulates
1. The area of a square is the square of the lengt
6.2 Inverses/Contrapositives
- conditional statement: if p then q, p implies q, q if p, p only if q
-converse if q then p
-Inverse statement- If not p then not q (not means it is not true that)
-Contrapositive- if not q then not p
-logically equivalent st
9.1 Introduction to Circles
-A circle is the set of coplanar points that are equidistant from a given oint
-the fixed point is the center
-the center is used to name the ircle
-radius- a segment whose endpoints are the center of the circle and any point o
2.1 Conditionals and Converses
-A conditional statement- a statement with a premise (hypothesis) and a conclusion. If the
statement is trye, then the conclusion is based on the premise
-Any conditional statement can be written in the if-then form
Let P: p
3.1 Introduction to Parallel Lines
-Parallel lines- coplanar lines that do not intersect
-parallelism also applies to rays and segments- It is possible for rays and segments to not
intersect and not be parallel
-Skew lines- non-coplanar lines that do not
5.1 Properties of Parallelograms
-Definition of a parallelogram- a convex quadrilateral with both pairs of opposite sides parallel
-Theorem- if a convex quadrilateral is a parallelogram, then both sides of opposite sides are
congruent
-Theorem- if a conve
1.2 Points, Lines, and Planes
-The undefined terms of Euclidian geometry:
1. Point- not concrete, simplest of geometric concepts, no size, no shape- so cant be measured
2. Lines- a collection of infinitely many points extending without end in opposite dir
12.1 Prisms
- a prism is a solid figure with 2 bases and n lateral bases where n is the number of sides of the
bases
-the bases of the prisms are congruent polygons in parallel planes
-the altitude of a prism is the vertical distance between the parallel
8.1 Similar Right Triangles
-Theorem- if an altitude is drawn to the hypotenuse of a right triangle, then 3 similar triangles
are formed, shown by angle-angle similarity
-Corollaries:
-when the altitude is drawn to the hypotenuse of a right triangle the l
7.1 Ratios and Proportions
-a ratio is a comparison of 2 or more numbers by division- 2 numbers or a:b
-3 or more numbers- a:b:c:d
-to compare values, all values must be in the same units
- b, c are the means and a,d are the extremes, a proportion is two