Basic Geometry Review Unit 3 Lesson 1 We will be identifying basic geometric terms. Objectives:  I can Identify and model points, lines, planes, and angles.  I can Identify intersecting lines and planes.

A B

line  A line has an arrowhead at each end line  A line can be named by a lowercase letter OR if two points are known, then the line can be named by those letters.  Called line n, line AB or AB, line BA or BA  We can also represent a line like: AB A B n

A B

C

 X  Y  Z T

 Drawn as a shaded, slanted 4-sided figure  Named as a capital letter or by using three non collinear points on that plane.  What could we name this plane?  Plane T, plane XYZ, plane XZY, plane YXZ, plane YZX, plane ZXY, plane ZYX.  X  Y  Z T

Lesson 1-1 Point, Line, Plane 10 Different planes in a figure: A B CD E F G H Plane ABCD Plane EFGH Plane BCGF Plane ADHE Plane ABFE Plane CDHG Etc.

A B D C M

 Noncoplanar points are points not in the same plane.

Modeling Points, Lines, and Planes Let’s take a look at a piece of paper

Naming Lines and Planes 1.Name a line containing point A. 2.Name a plane containing point C 3.Name three points that are collinear. 4. Are points E, A, B, and D collinear or non collinear? E l D C B A N

FACTS  It takes at least two points to make a line.  It takes at least three points to make a plane.  Space is the set of all points.

1. Are points A, B, and C collinear or noncollinear? 2. Are points B, C, and E collinear or noncollinear? 3. What are some ways to name this line? A E B C

Draw and label a figure for the following situation. Plane R contains lines AB and DE, which intersect at point P. Add point C on plane R so that it is not collinear with AB or DE. Example

A.B. C.D. Example Choose the best diagram for the given relationship. Plane D contains line a, line m, and line t, with all three lines intersecting at point Z. Also point F is on plane D and is not collinear with any of the three given lines.

 A line and a plane intersect at a point. P K

 Planes intersect at a line.

True or False 1. Line PF ends at P. 2. Point S is on an infinite number of lines. 3. The edge of a plane is a line. false true false

Example 1 Interpret Drawings A. How many planes appear in this figure? Answer: There are two planes: plane S and plane ABC.

Example 1 Interpret Drawings B. Name three points that are collinear. Answer: Points A, B, and D are collinear.

Example 1 Interpret Drawings C. Are points A, B, C, and D coplanar? Explain. Answer: Points A, B, C, and D all lie in plane ABC, so they are coplanar.

Example 1 Interpret Drawings Answer: The two lines intersect at point A.

A. A B. B C. C D. D 1) A.point X B.point N C.point R D.point A

2) Draw a surface to represent plane R and label it.

ANSWER 2) Draw a surface to represent plane R and label it.

Congruent Congruent refers to objects that have the same shape or size. *Congruent segments are segments that have equal length! ≅ When writing and signifying congruence, we use the ≅ symbol. When drawing a picture of figures that are congruent, we use slashes or ticks.

31 Congruent Segments Definition: If numbers are equal the objects are congruent. AB: the segment AB ( an object ) AB: the distance from A to B ( a number ) Congruent segments can be marked with dashes. Correct notation: Incorrect notation: Segments with equal lengths. (congruent symbol: )

Congruent Segments

Segment Bisector Any segment, line or plane that divides a segment into two congruent parts is called segment bisector. Definition:

Segment Bisector Any segment line or plane that intersects a segment at it’s midpoint. If X is between A and B and X is the midpoint of AB, what is the measure of AX if AB = 16x – 6 and XB = 4x + 9 ?

Ray Definition: ( the symbol RA is read as “ray RA” ) How to sketch: How to name: RA : RA and all points Y such that A is between R and Y.

Opposite Rays Definition: ( Opposite rays must have the same “endpoint” ) opposite raysnot opposite rays If A is between X and Y, then ray AX and ray AY are opposite rays.

Angles  An Angle is a figure formed by two rays with a common endpoint, called the vertex. vertex ray Angles can have points in the interior, in the exterior or on the angle. Points A, B and C are on the angle. D is in the interior and E is in the exterior. B is the vertex. A B C D E

(1) Using 3 points (2) Using 1 point (3) Using a number – next slide Using 3 points:vertex must be the middle letter This angle can be named as Using 1 point:using only vertex letter * Use this method is permitted when the vertex point is the vertex of one and only one angle. Since B is the vertex of only this angle, this can also be called. A B C Naming an angle

Naming an Angle - continued Using a number:A number (without a degree symbol) may be used as the label or name of the angle. This number is placed in the interior of the angle near its vertex. The angle to the left can be named as. * The “1 letter” name is unacceptable when … more than one angle has the same vertex point. In this case, use the three letter name or a number if it is present. 2 A BC

Example Therefore, there is NO in this diagram. There is K is the vertex of more than one angle.

4 Types of Angles Acute Angle: an angle whose measure is less than 90 . Right Angle: an angle whose measure is exactly 90 . Obtuse Angle: an angle whose measure is between 90  and 180 . Straight Angle: an angle that is exactly 180 .

Measuring Angles l Just as we can measure segments, we can also measure angles. l We use units called degrees to measure angles.  A circle measures _____  A (semi) half-circle measures _____  A quarter-circle measures _____  One degree is the angle measure of 1/360th of a circle. ? ? ? 360º 180º 90º

Adding Angles When you want to add angles, use the notation m  1, meaning the measure of  1. If you add m  1 + m  2, what is your result? m  1 + m  2 = 58 . Therefore, m  ADC = 58 . m  1 + m  2 = m  ADC also.

Angle Bisector An angle bisector is a ray in the interior of an angle that splits the angle into two congruent angles. 5 3 Example: Since  4   6, is an angle bisector.

Example  Draw your own diagram and answer this question:  If is the angle bisector of  PMY and m  PML = 87 , then find:  m  PMY = _______  m  LMY = _______

 3   5. Congruent Angles 5 3 Definition: If two angles have the same measure, then they are congruent. Congruent angles are marked with the same number of “arcs”. The symbol for congruence is ≅ Example:

Example  Draw your own diagram and answer this question:  If is the angle bisector of  PMY and m  PML = 87 , then find:  m  PMY = _______  m  LMY = _______

Practice Name all angles that have B as a vertex.