Geometry Geo + metry earth to measure

Three basic terms: point line plane

A point shows an exact location in space and is represented by a dot. Figure Name point A Symbol A A point shows an exact location in space and is represented by a dot. Description

A line is a set of points that extends infinitely in both directions. Figure Name line BC Symbol BC A line is a set of points that extends infinitely in both directions. Description

B C A Figure Name plane ABC Symbol plane ABC

A plane is a flat surface that extends infinitely in all directions. B C A Figure A plane is a flat surface that extends infinitely in all directions. Description

G H Figure Name segment GH Symbol GH A segment is part of a line consisting of two endpoints and all the points between them. Description

J K Figure Name ray JK Symbol JK A ray is part of a line consisting of one endpoint and extending infinitely through a second named point. Description

Example 1 Name all of the possible points, lines, planes, segments, and rays in the figure using the letters X, Y, and Z. X Y Z

X Y Z Points: X, Y, Z Lines: XY, YZ, XZ Planes: plane XYZ Segments: XY, YZ, XZ Rays: XY, YX, YZ, ZY, XZ, ZX

Example Name a line. E D A B C AB, BC, or AC

Example Name four rays with endpoint B. E D A B C BA, BD, BE, and BC

No, the endpoint is listed first. EB is not shown in the figure. Example Are rays BE and EB the same ray? E D A B C No, the endpoint is listed first. EB is not shown in the figure.

Angle An angle is a geometric figure made up of two rays that have a common endpoint. The common endpoint is the vertex. Each of the rays is a side of the angle.

A B C

Measuring an Angle Position the center point of the protractor on the vertex of the angle to be measured. Align the zero degree mark on the protractor with one side of the angle.

Measuring an Angle 3. Read the number of degrees to the other side of the angle on the protractor.

X acute angle m X < 90°

Y right angle m Y = 90°

obtuse angle 90° < m Z < 180°

W straight angle m W = 180°

6; ABD, DBE, EBC, ABE, DBC, and ABC Example How many angles are there in the figure? List them. E D A B C 6; ABD, DBE, EBC, ABE, DBC, and ABC

Example Classify ABE as acute, obtuse, right, or straight. E D A B C

Example Classify DBE as acute, obtuse, right, or straight. E D A B C

Example Classify ABC as acute, obtuse, right, or straight. E D A B C

Example Classify DBC as acute, obtuse, right, or straight. E D A B C

Example 2 Find the measure of DAE. C D B A E m DAE = 50°

Example 2 Find the measure of CAE. C D B A E m CAE = 125°

Example 2 Find the measure of BAC. C D B A E m BAC = 55°

Example 2 Find the measure of BAE. C D B A E m BAE = 180°

Example 3 Name all acute angles. E 35° 120° 25° F G H GEH, GEF, FEH, H, FGE

Example 3 Name a right angle. E 35° 120° 25° F G H F

Example 3 Name an obtuse angle. E 35° 120° 25° F G H EGH

Example 3 Name a straight angle. E 35° 120° 25° F G H FGH

Example 4 If m WYZ = 23°, write and solve an equation to find m XYW. m XYZ + 23 = 57 X – 23 57° m XYZ = 34° W 23° Y Z

Example If DBC is 138°, what is the measure of ABD? E D A B C 42°

Example If DBC is 138°, what is the measure of DBE? E D A B C 48°

Exercise How many lines can be drawn to connect two different points? 1

Exercise How many lines can be drawn to connect any two of three points that are not on the same line? 3

Exercise How many lines can be drawn to connect any two of four points, no three of which are on the same line? 6

Exercise How many lines can be drawn to connect any two of five points, no three of which are on the same line? 10

Exercise How many lines can be drawn to connect any two of six points, no three of which are on the same line? 15