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Date: ______________________

Section 1 – 1: Points, Lines, and Planes Notes

A Point: is simply a _______________. Example:

Drawn as a ________.

Named by a ______________ letter.

Words/Symbols:

A Line: is made up of ____________ and has no thickness or __________.

Drawn with an _________________ at each end.

Named by the _____________ representing two points on the line or a lowercase

script letter.

Points on the same _______ are said to be _____________.

Words/Symbols: Example:

A Plane: is a _______ surface made up of ____________.

Drawn as a ____________ 4-sided figure.

Named by a _____________ script letter or by the letters naming three

___________________ points.

Points that lie on the same plane are said to be _______________.

Words/Symbols: Example:

Example #1: Use the figure to name each of the following.

a.) Name a line that contains point P.

b.) Name the plane that contains lines n and m.

c.) Name the intersection of lines n and m.

d.) Name a point not on a line.

e.) What is another name for line n.

f.) Does line l intersect line n or line m? Explain.

Example #2: Draw and label a figure for the following relationship.

a.) Point T lies on WR. b.) AB intersects CD in plane Q at point P.

Example #3:

a.) How many planes appear in this figure?

b.) Name three points that are collinear.

c.) Are points A, B, C, and D coplanar? Explain.

d.) At what point do and CA intersect? DBsuur suur

2

Date: ______________________

Section 1 – 2: Linear Measure Notes – Part 1

Measure Line Segments

A line segment, or ______________, is a measurable part of a line that consists of

two points, called _________________, and all of the points between them.

A segment with endpoints A and B can be named as _______ or _______.

The length or _______________ of AB is written as ________.

Example #1: Use a metric ruler to draw each segment.

a.) Draw LM that is 42 millimeters long.

b.) Draw QR that is 5 centimeters long.

Example #2: Use a customary ruler to draw each segment.

a.) Draw DE that is 3 inches long.

b.) Draw FG that is 2 34

inches long.

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Calculate Measures

Betweenness of Points: Point M is between points P and

Q if and only if P,Q, and M are ______________ and

__________________.

Example #4:

a.) Find LM. b.) Find XZ.

c.) Find DE.

d.) Find x and ST if T is between S and U, ST = 7x, SU = 45, and TU = 5x – 3.

e.) Find y and PQ if P is between Q and R, PQ = 2y, QR = 3y + 1, and PR = 21. Draw a picture!

2

Date: ______________________

Section 1 – 2: Linear Measure Notes – Part 2

Example: Find the value of x and LM if L is between N and M, NL = 6x – 5,

LM = 2x + 3, and NM = 30. Draw a picture!

Measure Line Segments

Key Concept (Congruent Segments):

Two __________________ having the same Ex:

measure are __________________.

Symbol:

Example #1: Name all of the congruent segments found in the kite.

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Example #2: Find the measurement of RS.

Example #3: Use the figures to determine whether each pair of segments is congruent.

a.) ,AB CD b.) ,WZ XY

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c.) ,HO HT d.) ,MH TH

Date: ______________________

Section 1 – 3: Distance Notes – Part 1

Distance Between Two Points Key Concept (Distance Formulas):

Number Line

Coordinate Plane

The distance d between two points with coordinates (x1, y1) and (x2, y2) is given by

d =

Pythagorean Theorem: Example #1: Find the distance between E(-4, 1) and F(3, -1). Hint: Draw a triangle!

1

Example #2: Use the number line to find QR.

Example #3: Use the number line to find CD.

Example #4: Use the number line to find AB and CD.

Example #5: Use the Distance Formula to find the distance between the following points.

a.) A(10, -2) and B(13, -7)

b.) X(-5, -7) and Y(-10, 7)

c.) G(-4, 1) and H(3, -1)

2

Date: ______________________

Section 1 – 3: Midpoint Notes – Part 2

Midpoint of a Segment

Key Concept (Midpoint):

The midpoint M of PQ is the point ___________________ P and Q such that

_____________________.

Number Line: The coordinate of the

midpoint of a __________________ whose

endpoints have coordinates a and b is

Example #1: The coordinates on a number line of J and K are –12 and 16, respectively. Find the

coordinate of the midpoint of JK . Hint: Draw a number line!

Example #2: The coordinates on a number line of T and S are 5 and 8, respectively. Find the

coordinate of the midpoint of TS . Hint: Draw a number line!

Coordinate Plane: The coordinates of the

_____________________ of a segment

whose endpoints have coordinates (x1, y1)

and (x2, y2) are

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Example #3: Find the coordinates of the midpoint of PQ for P(-1, 2) and Q(6, 1). Example #4: Find the coordinates of the midpoint of GH for G(8, -6) and H(-14, 12). Example #5: Find the coordinates of the midpoint of AB for A(4, 2) and B(8, -6). Example #6: What is the measure of PR if Q is the midpoint of PR ? Segment Bisector: any segment, line, or plane that interests a

segment at its _______________

2

Date: ______________________

Section 1 – 4: Angle Measure Notes – Part 1

Measure Angles

Degree: a unit of measure used in measuring

______________ and __________. An arc of a

circle with a measure of 1° is ___________ of the

entire circle.

Ray: is a part of a ___________

It has one ____________________ and extends

indefinitely in _________ direction.

Symbols:

Opposite Rays: two rays _________ and _________

such that B is between A and C

Key Concept (Angle):

An angle is formed by two ______________________ rays that have a common

__________________.

The rays are called ____________ of the angle.

The common endpoint is the ______________.

Symbols:

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An angle divides a plane into three distinct parts.

Points _____, _____, and _____ lie on the angle.

Points _____ and _____ lie in the interior of the

angle.

Points _____ and _____ lie in the exterior of the angle.

Example #1:

a.) Name all angles that have B as a vertex.

b.) Name the sides of 5∠ .

c.) Write another name for . 6∠

Example #2:

a.) Name all the angles that have W as a vertex.

b.) Name the sides of 1∠ .

c.) Write another name for WYZ∠ .

d.) Name the vertex of . 4∠

2

Date: ______________________

Section 1 – 4: Angle Measure Notes – Part 2

Measure Angles

Key Concept (Classify Angles):

RIGHT ANGLE: ACUTE ANGLE: OBTUSE ANGLE:

Model: Model: Model:

Measure: Measure: Measure:

Example #1: Measure each angle, then classify as right, acute, or obtuse.

a.) b.)

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c.) d.)

e.) f.)

Example #2: Measure each angle named and classify it as right, acute, or obtuse.

a.) TYV∠

b.) WYT∠

c.) TYU∠

d.) VYX∠

e.) SYV∠

2

Date: ______________________

Section 1 – 4: Angle Measure Notes – Part 3

Congruent Angles

Key Concept (Congruent Angles):

Angles that have the same _____________________ are

congruent angles.

Arcs on the figure also indicate which angles are

___________________.

Example #1: State whether each pair of angles is congruent, and if so write a congruence statement.

a.) b.)

Example #2: Find the value of x and the measure of one angle.

1

Angle Bisector: a _________ that divides an angle into _________ congruent angles.

Ex:

If PQuuur

is the angle bisector of ___________,

then _____________________.

Example #3: In the figure, QP and QR are opposite rays, and QT bisects . RQS∠

a.) If and 56 +=∠ xRQTm 27 −=∠ xSQTm , find RQTm∠ .

b.) Find if and TQSm∠ 1122 −=∠ aRQSm 812 −=∠ aRQTm .

Example #4: In the figure, YU bisects ZYW∠ and YT bisects XYW∠ .

a.) If and , find 1051 +=∠ xm 2382 −=∠ xm 2∠m .

b.) If =82 and , find r. WYZm∠ 254 +=∠ rZYUm

2

Date: ______________________

Section 1 – 5: Angle Relationships Notes – Part 1

Pairs of Angles

Key Concept (Angle Pairs):

Adjacent Angles: are two angles that lie in the same ____________, have a common

_____________, and a common ___________, but no common interior ____________

Examples:

Vertical Angles : are two non-adjacent angles formed by two __________________ lines

Examples: Non-example:

Linear Pair : a pair of ________________ angles whose non-common sides are opposite

__________.

Example: Non-example:

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Example #1 : Name an angle pair that satisfies each condition.

a.) two angles that form a linear pair

b.) two acute vertical angles

c.) an angle supplementary to VZX∠

d.) two acute adjacent angles

Key Concept (Angle Relationships):

Complementary Angles: two angles whose measures have a sum of ________

Examples:

Supplementary Angles: two angles whose measures have a sum of ________.

Examples:

Example #2: Find the measures of two supplementary angles if the measure of one angle is 6 less

than 5 times the measure of the other angle.

Example #3: Find the measures of two complementary angles if the difference in the measures of the

two angles is 12.

Example #4: The measure of an angle’s supplement is 33 less than the measure of the angle. Find the

measure of the angle and its supplement.

2

Date: ______________________

Section 1 – 5: Angle Relationships Notes – Part 2

Perpendicular Lines

Lines that form right angles are _____________________.

Key Concept (Perpendicular Lines):

Perpendicular lines intersect to form _________ right

angles.

Perpendicular lines intersect to form _________________

_______________ angles.

________________ and _________ can be perpendicular

to lines or to other line segments and rays.

The right angle symbol in the figure indicates that the lines are ___________________.

Symbol: _______ is read is perpendicular to.

Example #1: Find x so that . KO HM⊥suur suuur

Example #2: Find x and y so that BE and AD are perpendicular.

1

Assumptions:

Example #3: Determine whether or not each of the following statements can be assumed or not.

All points shown are coplanar.

P is between L and Q.

PLPN ≅

QPO∠ and OPL∠ are supplementary.

PMPN ⊥

L, P, and Q are collinear.

LPM QPO ∠≅∠

POPQ ≅

PQLP ≅

LMP∠ and MNP∠ are adjacent angles.

LPN∠ and NPQ∠ are a linear pair.

LPM OPN ∠≅∠

,,, POPNPM and LQ intersect at P.

Example #4: Determine whether each statement can be assumed from the figure below. Explain.

a.) 90m VYT∠ =

b.) and are supplementary TYW∠ TYU∠

c.) and are complementary VYW∠ TYS∠

2

Date: ______________________

Section 1 – 5: Angle Relationships Extra Examples

Example #1: Two angles are complementary. One angle measures 24° more than the other. Find the measures of the angles. Example #2: Find the measures of two supplementary angles if the measure of one angle is 4 less than 3 times the measure of the other angle. Example #3: The measure of an angle’s supplement is 22 less than the measure of the angle. Find the measure of the angle and its supplement. Example #4: Find the value of x so that AC

suur and BD

suur are perpendicular.

1

Date: ______________________

Section 1 – 6: Polygons Notes

Polygons

A polygon is a ______________ figure whose sides are all segments.

The sides of each angle in a polygon are called ___________ of the polygon, and the vertex of

each angle is a _____________ of the polygon.

Examples:

Polygons can be ________________ or ________________.

Examples:

_____________________ ________________________

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Regular Polygon: a convex

polygon in which all the ________

are congruent and all the angles are

___________________.

Number of Sides Polygon

Ex:

2

3 quadrilateral 5 6 heptagon octagon 9 decagon

12 n

Example #1: Name each polygon by the number of sides. Then classify it as convex or concave, regular

or irregular.

a.) b.)

Perimeter

The perimeter of a polygon is the sum of the _______________ of its sides, which are

_________________.

Example #2: Find the perimeter of each polygon.

a.) b.) c.)