Notes: Identify Points, Lines, and Planes 1.1

Objective: Name and sketch geometric figures

Write in words what each of the following symbols means.

1) PL 2) GD 3) M 4) KJ

Name the following figures.

5) 6)

7) 8)

9) Name a pair of opposite rays in the following picture

10) Collinear points are points that _____________________________________ .

11) Coplanar points are points that ______________________________________ .

Use the picture below for questions 12 – 15.

12) Give two other names for BD 13) Give another name for plane T

14) Name three points that are collinear. Then name a fourth point that is not collinear with those

three points.

15) Name a point that is NOT coplanar with E, C, and A.

Notes: Identify Points, Lines, and Planes 1.1

Use the picture below for questions 16 – 19.

16) Give another name for ST 17) Name all rays with endpoint Q

18) Name two pairs of opposite rays 19) Give another name for PR

Use the picture below for questions 20 – 21.

20) Name the intersection of plane PQS and plane HGS.

21) Are points P and G collinear? Are they coplanar?

22) Sketch two lines that lie in a plane and intersect at one point.

23) Sketch two lines that lie in a plane, and one line that does not lie in the plane.

You are given an equation of a line and a point. Use substitution to determine whether the point

is on the line.

24) )1,5(;4 Axy 25) )1,7(;43 Axy

Graph the inequality on a number line. Tell whether the graph is a segment, ray, point, or line.

26) 3x 27) 47 xorx

Notes: Use Segments and Congruence 1.2

Objective: Use segment postulates to identify congruent segments

1) XY means ______________________________

2) XY means ______________________________

3) Find RT 4) Find BC

Plot the following points in a coordinate plane. Then determine whether the line segments

named are congruent.

5) 6)

Use the number line to find the indicated measure.

7) AB 8) CE 9) AE 10) BD

Notes: Use Segments and Congruence 1.2

In the diagram, points V, W, X, Y, and Z are collinear, VZ = 50, XZ = 22, and WX = XY = YZ.

Find the indicated length.

11) WX 12) VW

13) WY 14) VX

15) WZ 16) VY

17) 18)

Notes: Use Midpoint and Distance Formulas 1.3

Objective: Find lengths of segments in the coordinate plane

Midpoint Formula

If ),( 11 yxA and ),( 22 yxB are two points in a coordinate plane, then the midpoint of AB is

1) Find the midpoint of the segment graphed below.

Find the coordinates of the midpoint of the segment with the given endpoints.

2) E(-7, -5) and F(-3, 7) 3) J(-8, -7) and K(11, 5)

Use the given endpoint J and midpoint M of JK to find the coordinates of the other endpoint K.

4) J(1, 4), M(2, 1) 5) J(5, 1), M(1, 4) 6) J(6, -2), M(5, 3)

Notes: Use Midpoint and Distance Formulas 1.3

A midpoint ______________________________________________________ .

A segment bisector _______________________________________________________ .

A segment bisector can be a point, ray, line, line segment, or plane.

Line bisects the segment. Find the indicated length.

7) Find RS 8) Find BC if AC = 19 cm

9) Find QR if PR = .2

19 in 10) Find UW if VW = mm

8

3

In each diagram, M is the midpoint of the segment. Find the indicated length.

11) Find LN 12) Find AM

Notes: Use Midpoint and Distance Formulas 1.3

Distance Formula If ),( 11 yxA and ),( 22 yxB are two points in a coordinate plane, then the distance between A & B is

**The distance between points A and B is the same as the length of the segment AB.

Find the length of each segment.

13)

14)

Find the distance between the following points (same as finding the length of the segment).

15) A(0, 2) and B(-3, 8) 16) C(-4, 2) and D(3, -7)

Notes: Measure and Classify Angles 1.4

Objective: Name, measure, and classify angles

Write three names for the angle shown. Then name the vertex and sides of the angle. 1) 2) 3) Name three different angles in the diagram below. Give another name for the angle in the diagram below. Tell whether the angle appears to be acute, right, obtuse, or straight. 4) JKN 5) KMN 6) PQM 7) KLP Find the indicated angle measure. 8) ______QSTm

Notes: Measure and Classify Angles 1.4

Use the given information to find the indicated angle measure. 9) Given ,80WXZm find YXZm Find the indicated angle measure. 10) a 11) b 12) c 13) d In each diagram, BD bisects ABC . Find ABCm . 14) 15)

Notes: Describe Angle Pair Relationships 1.5

Objective: Use special angle relationships to find angle measures Two angles are complementary angles if their measures add to ____________ . Two angles are supplementary angles if their measures add to ____________ . Two angles that share a common vertex and side are called _______________________ .

1) Name a pair of complementary angles and a pair of supplementary angles.

1 and 2 are complementary angles. Given the measure of 1 , find 2m 2) 521m 3) 81m

1 and 2 are supplementary angles. Given the measure of 1 , find 2m 4) 1031m 5) 321m Find ABCm and CBDm . 6) 7)

Notes: Describe Angle Pair Relationships 1.5

1 and 2 are a ___________________ . 3 and 6 are _____________________ .

Their measures ____________________ . Their measures ______________________ .

Tell whether the angles are vertical angles, a linear pair, or neither. 8) 31 and 9) 85 and 10) 32 and 11) 94 and 12) 65 and 13) 76 and 14) Two angles form a linear pair. The measure of one angle is 3 times the measure of the other angle. Find the measure of each angle. Find the values of x and y. 15) 16)

Notes: Classify Polygons 1.6

Objective: Classify polygons

A polygon is a closed figure with the following properties:

It is formed by three or more line segments

Each side intersects exactly 2 sides

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

1) 2) 3) 4)

Equilateral: _______________ Equiangular: _____________ Regular: ___________

Classify the polygon by the number of sides. Tell whether the polygon is equilateral,

equiangular, or regular.

5) 6) 7)

Notes: Classify Polygons 1.6

8) The lengths of two sides of a regular pentagon are represented by the expressions 275 x and

62 x . Find the length of a side of the pentagon.

9) The expressions )633( x and )457( x represent the measures of two angles of a regular

decagon. Find the measure of an angle of the decagon.

Each figure is a regular polygon. Expressions are given for two side lengths. Find the value of x.

10)

Notes: Find Perimeter, Circumference, and Area 1.7 Objective: Calculate dimensions of polygons

Define the following terms on your vocabulary sheet: Perimeter, Circumference, Area, Diameter, Radius

Find the perimeter (or circumference) and area of each figure.

1. 2.

Give your answers in terms of .

3. 4.

Notes: Find Perimeter, Circumference, and Area 1.7 5.

Find the perimeter of the figure. Round to the nearest tenth of a unit.

6.

Use the information about the figure to find the indicated measure.

7. Area = 308 2m 8. Area = 264 2ft

Find the height h. Find the base b

b

9. Perimeter = 31 in.

Find the width w.