1st Quarter Geometry Test Name: Date:
1.) Using the simple interest formula (I=Prt), how much will you have in your account after three years if you deposit $2500 into an account that earns 8% interest? a. $600 b. $3100 c. $8500 d. $60000
2.) A scale mode
Opposite Parts of a Parallelogram:
X W WCh 2 Section 5 Parallelograms X Z Y Y Z . .
The opposite The
of a parallelogram are of a parallelogram are
I f is a
then,
and
.
Ifis a
then,
and
.
Complete the following table using your book. Term Definition A quad
2.1 Homework and Review Find the measure of each angle in the diagram at the right. Tell which properties or definitions you use.
Given:
C 110 B
D 150 E G F A 40
1.) FAB
2.) CDB
3.) EDF
4.) CBD
5.) BDF
6.) DEF
7.) EFG
8.) CBA
Find the measures of the comp
2.1 HW assessment NAME: Matching. 1.) non-adjacent, non-overlapping angles formed by two intersecting lines.
2
1
2.)
two angles with measures that add up to 90
40
50
3.)
two coplanar angles that share a vertex and a side but do not overlap.
3
4
4.)
two an
Ch 2 Section 1 Classifying Triangles Triangle (p. 64) - the figure formed by the segments whose endpoints are three points. Example:
Sides (p. 65) - the segments that form a triangle Example:
Vertices (p. 65) - the endpoints of the sides of a triangle (si
Name:
1. 2. 3. 4. 5. 6.
Consecutive angles Consecutive sides Diagonal Regular Equiangular Equilateral
a.) two sides that share a vertex b.) a polygon that is both equilateral and equiangular c.) a segment that connects nonconsecutive vertices d.) two angl
Ch 2 section 3 Types of Polygons Complete Think and Communicate page 72. 1.) 2.) 3a.)
b.)
Polygon (p. 73) - a intersect only at their
plane figure whose sides are .
that
Triangle (p. 73) - a polygon with
sides
Quadrilateral (p. 73) - a polygon with GOAL P
Ch 2 section 4 Angles in Polygons Exploration (page 79). Complete the Type of polygon Number of sides Number of triangles formed Sum of angle measures of all the triangles Sum of the angle measures of the polygon
Triangle Quadrilateral Pentagon Hexagon He
Interior angles
X Y Ch2 Section 4 Angles in Polygons W Z interi or angles
Using the information you gathered develop a formula to find the sum of the angles of a polygon.
The Angles of a Polygon In a is with n sides, the sum of the .
The angles we just lo
2.6 Building Prisms
Term Prism
Definition a _ dimensional figure with _ congruent faces that are polygons that lie in parallel planes
Base
one of the _ parallel faces of a prism A face of a _ that is not a base (These faces are formed by connecting corres
Ch 2 Section 5 Opposite Parts of a Parallelogram: The opposite The of a parallelogram are of a parallelogram are . .
If is a
then,
and
.
Ifis a
then,
and Complete the following table using your book. Term Definition
.
Example
A quadrilateral with both pai
Ch 3 Section 1 Inductive and Deductive Reasoning Think and Communicate (page 111) 1.)
2.)
Inductive Reasoning: Example1: If it rains tonight, then it will be foggy in the morning. Deductive reasoning: involves using , and accepted properties in a Example
3.2 Postulates, Definitions, and properties
Postulate - a
STATEMENT
that is accepted without
PROOF
.
Sketch the following: If pt. Y is between pts. X and Z, then X, Y, and Z are collinear and XY + YZ = XZ
Definition- the meaning of a word. An obtuse angle
3.2 Postulates, Definitions, and properties
Postulate - a Sketch the following.
that is accepted without
.
If pt. Y is between pts. X and Z, then X, Y, and Z are collinear and XY + YZ = XZ
Definition- the meaning of a word. An obtuse angle is an angle tha
Chapter 3 section 3 Proof - a chain of in which statements are placed in a logical order, with a
reason that everyone agrees is true given for each statement Theorem- a that can be proved to be true
Paragraph proof- a proof that is written in Statement- t
Ch3 sec 4
Two-Column Proofs Two-column proof a proof format that contains statements and reasons arranged in two columns. Example 1 Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that
Ch 3 sections 4, 5, and 7 Two-Column Proofs Two-column proof a proof format that contains statements and reasons arranged in two columns. Example 1 Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two inte
Ch 3 sec 6 Pages 141-147 Pythagorean Theorem Leg- in a right triangle, each of the two shorter sides. Hypotenuse- in a right triangle, the side Proof of the Pythagorean theorem- Exploration (page 141) 2.)Area of the Square = the right angle
Triangle 1 2 3
4.1 Examples Find the lengths of the sides of the polygon whose vertices are given. Give the most specific name for the polygon. 1. F(0, 1), G(6, 2), H(6, 4) FG= FG= FG= FG= GH= GH= GH= GH= FH= FH= FH= FH= 12. Q(2, 1), R(1, 4), S(4, 1), T(1, 2) QR= QR= QR
Slope, Parallelism, & Perpendicularity
Given a line in the plane, the ratio of the change in y to the change in x as you move from left to right is the slope of the line. If a line passes through two distinct points P1(x1, y1) and P2(x2, y2) where x1 give
C hapter 4 Vocabula ry
slope:
y-intercept:
slope-intercept form:
perpendicula r bisector:
circle:
diameter of a circle:
r ad ius ( r adi i):
concent ric circles:
coordinate geometry proof:
three dimensional coordinate system:
z-axis:
ordered t r iple (x,
4.2 Equations of Lines The Slope Formula-(fill in the blanks and include all sketches or drawings) The , ) is: (m) of a containing the points ( , ) and (
m= The slope of a The is of a . line is line .
Checking Key Concepts page 176
1.)
= = Sketch the situ
Chapter 4 Section 3 Exploring Parallels and Perpendiculars Perpendicular bisector (p. 181) - A line, ray, or segment that intersects a given segment at it in Example: . and divides
Slopes of parallel and perpendicular lines
Parallel Lines Theorem: If two
NAME: Tell whether each pair of lines is parallel, perpendicular, or neither. 1.) y = 3/4 x + 2 y = - 4/3 x + 2 2.) y = 4x + 6 y = 4x - 3
Find the slope of each line. 3. a line perpendicular to the line y = 3x + 2 4. a horizontal line that crosses the y-a
5.1 Parallel lines and Transversals Transversal- a line that intersects two or more lines in the same plane at different points.
Same side interior angles- angles that lie on the same side of a transversal between the two lines it intersects.
Alternate in
5.2 Properties of Parallel Lines Think and Communicate (page 226) 1.)
2.)
Alternate Interior Angles Theorem If two parallel lines are intersected by a _, then alternate interior angles are _. Draw an example
If
, then
.
Think and Communicate (page 227) 3.
5.3 Types of Proofs Two Column Proof- A convincing argument organized into two columns (statements and reasons) that is used to show that a conjecture is true. Paragraph Proof A convincing argument written in complete sentences to show that a conjecture i
5.4 Conditions for Parallel Lines You can use converse statements to prove conjectures true. Converse of the Corresponding Angles Postulate- If 2 lines are intersected by a transversal and corresponding angles are congruent, then the 2 lines are _.
Conver
5.6 Parallels in Space Line perpendicular to a plane- A line that intersects the plane and is perpendicular to every line in the plane that passes through the point of intersection.
Distance from a point to a plane - The length of the perpendicular segmen
6.1 Triangle Inequalities
Side lengths of a triangle Triangle Inequality Theorem 1The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
In triangle ABC, AB + BC > AC, AB + AC > BC, and AC + BC > AB. Examples: