Name _____________________________________________________________________________ Hr ____

Honors Geometry 1-1: Identify Points, Lines, and Planes Learning Target: At the end of today’s lesson we will be able to successfully name and sketch geometric figures.

In Geometry there are 3 UNDEFINED TERMS. These words DO NOT have formal definitions, but there is agreement about what they mean.

1.) _________________ 2.) _________________ 3.) _________________Vocabulary Description Illustration

Point 1. A point has ____ dimension. 2. It is represented by a ______.

Name :

Line

1. Line A line has __________ dimension. 2. It is represented by a _________ with two arrowheads.3. It extends ____________ in two directions.4. Through any ________ points, there is exactly ____ line.5. You can use any _______ points on a line to name it or _________ case cursive letter. Name:

Plane

1. Has _____ dimensions. 2. It is represented by a shape thatlooks like a floor or wall, but it extends without end.3. Through any _____ points not on the same line, there is exactly _____ plane.4. You can use three points that are ______ all on the same line to name a plane.

Name:Collinear

PointsPoints on the same __________________.

Coplanar Points

Points on the same __________________.

Ex 1:

a. Give two other name for ______, ______

b. Give another name for plane Z. _______

c. Name three points that are collinear. _____, _____, _____

d. Name four points that are coplanar. _____, _____, _____, _____

Ex 2: Use the diagram in Example 1.

a. Give two other names for b. Name a point that is not coplanar with points L, N, and P.

LN

MQ

Line:

Line AB (written as ________) and points A and B are used here to define the terms below:Defined Terms

Description Illustration

SegmentThe line segment AB, or segment AB, (written as _________)

consists of the endpoints A and B and all points on that are _____________________________ A and B.

Ray

The ray AB (written as _____) consists of the endpoints A and all points on that lie on the same side of ________ as _______.

Note: and are two ____________________ rays!

Opposite Rays

If point C lines on line AB between A and B, then _________ and _________ are opposite rays.

Note: Opposite rays form a _____________________ angle!

Ex 3:a. Give another name for . ______ b. Name all rays with endpoints W. ______________________c. Which of these rays are opposite rays? ___________ & ___________

d. WX and WY have a common ________________________, but are not _______________. So they are not opposite rays.

e. Are and the same ray? Are and the same ray?

Intersecting Figures:The intersection of two or more geometric figures is the set of points that the figures have in_______________.

Description Sketch Intersection

Two crossing lines

Intersection of twodifferent planes

A plane and a linethat intersect in one spot

A plane and a line thatis in the plane

*** Ex 4 You are given two equations of lines and a point. Do the lines intersect at the given point? Explain your reasoning.

y = x + 8y = –4x – 3A(–2, 6)

Honors Geometry 1-2: Use Segments and Congruence/Use Distance and Midpoint Formulas

Learning Target: At the end of today’s lesson we will be able to successfully use segment postulates to identify congruent segments.

Postulate/Axiom: Theorem:In Geometry, a rule that is _______________ without proof. A rule that can be_________________________.

Postulate 1.1: The Ruler Postulate

The points on a line can be matched one to one with real numbers. The real number that corresponds to a point is the coordinate of the point.

Absolute value: The distance between points A and B, written as_______, is the absolute value of the _____________ of the coordinates of A and B.

AB is also called the ______________________ of AB .(Note: Absolute values are ALWAYS________________________.)

Ex 1: Measure the length of AB to the nearest tenth of a centimeter.

Ex 2: Use the number line to find each length below.

a) BD b) AC

Three Collinear Points:When three points are collinear, you can say that one point is _______________ the other two on the same line.

Postulate 1.2: The Segment Addition PostulateIf B is between A and C, then AB + BC = _______

If AB + BC = AC, then B is between _____ and _____

Ex 3: Find QS and PQ Ex 4:

***Ex 5: Point M is between L and N on LN . Use the given information to the write an equation in terms of x. Draw and label a picture of the situation, then algebraically solve for x. (Disregard any answers that do not make sense in the context of the problem). Then find LM and MN.

LM = x2

MN = x L M = _ _ _ _ _ _

LN = 56 M N =

Congruent Line Segments:Line segments that have the ___________ length.

Ex 6:

Plot F(-4, 5), G(–l, 1), H(1, –3), and J(4, 1) . Are FG

and HJ

congruent?

Honors Geometry 1-3: Use Distance and Midpoint Formulas

Learning Target: At the end of today’s lesson we will be able to successfully find lengths of segments in the coordinate plane.

Midpoint: The point that divides the segment into two CONGRUENT segments. If M is the midpoint of the segment, then

_____ _____ & _____ = _____

Segment Bisector:A point, line, line segment, or plane that intersects the segment at its_____________________.

_____ _____ & _____ = _____

Ex 1 : Point M is the midpoint of GH.

Ex 2: Line t is the segment bisector of PQ.

Midpoint FormulaThe coordinates of the midpoint of a segment are the ________________ of the x-coordinates and of the y-coordinates of the endpoints.

If A(x1,y1)and B(x2, y2) are points in a coordinate plane,

then the midpoint M of AB has coordinates: (Mx, My) =

Ex 3:

a) The endpoints of are P(–2, 5) and R(4, 3). b) The midpoint of AC is M(3, 4). One endpoint is A(l, 6). Find the coordinates of the midpoint M. Find the coordinates of endpoint C.

t

THE DISTANCE FORMULAIf A(x1, y1) and B(x2, y2) are points in a coordinate plane, then the distance between A and B is

Ex 4 : What is the approximate length of segment RT, with endpoints R(3, 2) and T(–4, 3)

Pythagorean Theorem:

In a right triangle, the square of the length of the hypotenuse is

equal to the sum of the squares of the lengths of the legs.

Ex 5: A 6 foot board rests under a doorknob and the base of the board is 5 feet away from the bottom of the door. Approximately how high above the ground is the doorknob?

***Ex 6: Multi-Step Problem The diagram shows existing roads ( E⃗G and ) and a proposed road being considered.

a. If you drive from point E to point H on existing roads, how far do you travel?

b. If you were to use the proposed road as you drive from E to H, about how far do you travel? Round to the nearest tenth of a mile.

c. About how much shorter is the trip if you were to use the proposed road?

Honors Geometry 1-4: Classify Polygons

Learning Target: At the end of today’s lesson we will be able to successfully classify polygons.

VOCABULARY

Polygon A polygon is a ___________ plane figure with the following properties: (1) It is formed by three or more line segments called___________. (2) Each side intersects exactly _____ sides, one at each endpoint, so that no two sides with a common endpoint are collinear.

Sides The sides of a polygon are the line ____________ that form the polygon.

Vertex A vertex of a polygon is an ___________ of a side of the polygon.

Convex A polygon is convex if no line that contains a side of the polygon contains a point in the interior of the polygon.

Concave A concave polygon is a polygon that is _____ convex

Ex 1: Tell whether the figure is a polygon and whether it is convex or concave.

Classifying Polygons by Sides

Formulas for Area and Perimeter Square: Rectangle:

Area of a Triangle

Acute Obtuse Right

Number of Sides

Type of Polygon

3   4   5   6   7  

Number of Sides

Type of Polygon

8  

9  

10  

12  

n  

(Note: The legs are the base & height)A = ___________________

Ex 2: : Find the area and perimeter of the figure. Show ALL formulas used! If necessary round to the nearest tenth.

Perimeter = Perimeter =

Area = Area =

Ex 3: Find the area of each triangle.

a) b)

Ex 3: The base of a triangle is 24 feet. Its area is 216 square feet. Find the height of the triangle.

Ex 4: Triangle JKL has vertices J (1, 6), K (6, 6), and L (3, 2). Find the approximate perimeter of triangle JKL.

***Ex 5: Use the figure shown and the Pythagorean Theorem to write a formula for the area A of an equilateral triangle with side x.

Honors Geometry 1-5 Measure and Classify Angles

Learning Target: At the end of today’s lesson we will be able to successfully name, measure, and classify angles.

Angle: Consists of two different _______ with the same endpoint:

The rays are the ________ of the angle.

The endpoint is the _________ of the angle.

The angle has sides _________ and _________.

The angle can be named _______, ________, or _________.

__________ is the vertex of the angle.

Ex 1: Name the three angles in the diagram below.

___________, ______________, ____________

Postulate 1.3: The Protractor Postulate

Classifying AnglesAcute Angle Right angle Obtuse angle Straight angle

Ex 2: Use the diagram to find the measure of the indicated angle. Then classify the angle.

ClassifymÐWSR =

mÐTSW =

mÐRST =

mÐVST =

Postulate 1.4: The Angle Addition Postulate

If D is in the interior of ÐABC, then the measure of ÐABC is equal to the sum of the measures of Ð________ and Ð_________.

If D is in the interior of ÐABC, then mÐABC = mÐ________+ mÐ________ = _____ +_____ = _______

Ex 3: Given that mÐGFJ = 155°, Ex 4: Given that ÐVRS is a right angle,find mÐGFH and mÐHFJ. find mÐVRT and mÐTRS.

Congruent Angles: Two angles are congruent if they have the __________ measure.

Ex 5: a.) Identify all pairs of congruent angles in the diagram.

b.) If mÐP = 120°, what is mÐN?

Angle Bisector:

A ray that divides an angle into two angles that are ________________.

Ex 6: Find x, ∠ABD∧∠DBC .

a) In the diagram, B⃗D bisects ∠ABC. b) In the diagram, ∠ABCis a straight angle.

Honors Geometry 1-6: Describe Angle Pair Relationships

Learning Target: At the end of today’s lesson we will be able to successfully use special angle relationships to find angle measures.

Angle Pair Relationships

Adjacent angles Two angles that share a common vertex and __________ but have no common interior points.

Complementary anglesTwo angles whose sum is _______°

Each angle is the _________________ of each other.

Supplementary anglesTwo angles whose sum is _______°

Each angle is the ________________ of each other.

Linear pairTwo _____________ angles are a linear pair if their noncommon sides are opposite rays.

Vertical anglesTwo angles are vertical angles if their sides form two pairs of _______________ rays.

Ex 1: a) Given that Ð1 is a complement of Ð2 and mÐ2 = 57°, find mÐ1.

b) Given that Ð3 is a supplement of Ð4 and mÐ4 = 41°, find mÐ3.

***c) Let Ð A and Ð B be supplementary angles and let mÐ A = (x2 + 12x)° and mÐ B = (3x2 + 20)°.

What is the value of x? x =

What are the measures of the angles? m ÐA =

m ÐB = _______

Ex 2:The basketball pole forms a pair of supplementary angles with the ground. Find mÐBCA and mÐDCA.

Ex 3:   Find mÐABC and mÐCBD for the figure.

mÐABC = ______ mÐCBD = ________

Ex 4:   a.)  Identify each in the figure below.

Linear pairs:_________________ Vertical angles:__________________

b.) ÐAreÐ1 and ÐÐ4 a linear pair? Explain why or why not.

Ex 5:a.) Two angles form a linear pair. The measure of one angle is 3 times the measure of the other. Find the measure of each angle.

b.) The measure of an angle is twice the measure of its complement. Find the measure of each angle.

There are some things you can conclude from a diagram, and some you cannot.

CAN CONCLUDE CANNOT CONCLUDEAll points shown are _____________________. AB≃BCPoints A, B, and C are _____________________________, and B is between A and C.

ÐDBE @ ÐEBC

A⃗C , B⃗D , B⃗E _____________________________________, at point B.

ÐABD is a right angle.

ÐDBE and ÐEBC are _________________ angles, and ÐABC is a ______________ _____________.Point E lies in the __________________ of ÐDBC.