introduction to geometry and measurements
DESCRIPTION
Covers topics on Defined and Undefined Terms, Angles and Kinds of Angles According to MeasurementTRANSCRIPT
![Page 1: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/1.jpg)
Introduction to Geometry &
Measurements
Roxanne Joie V. Deang
BSE Math IV
![Page 2: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/2.jpg)
POINTS, LINES, & PLANES
![Page 3: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/3.jpg)
POINTS
![Page 4: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/4.jpg)
Point
basic element in geometry represented by a dot (.)
an idea that shows an exact location in space
no dimension; no length; no width and no thickness
named using a capital letter
![Page 5: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/5.jpg)
LINES
![Page 6: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/6.jpg)
Line
set of infinite points extended endlessly or indefinitely in two directions
represented by a stretch string, edge of a table, etc.
it has one dimension which is the length named by one small letter or two capital
letters
![Page 7: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/7.jpg)
Name this line!
L O V E
![Page 8: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/8.jpg)
PLANES
![Page 9: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/9.jpg)
Plane
set of infinite points extended in four directions
it has two dimensions – length and width represented by any flat surface named by at least three points of the plane
provided that the points must not lie along the same line
![Page 10: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/10.jpg)
Name this
plane!
JV
A
RK
N
D
M
L
![Page 11: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/11.jpg)
RAYS & ANGLES
![Page 12: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/12.jpg)
RAYS
![Page 13: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/13.jpg)
Ray
a part of a line that extends indefinitely in one direction
named by writing the endpoint first and then another point on the ray
R O X
![Page 14: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/14.jpg)
ANGLES
![Page 15: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/15.jpg)
Angle
formed by two rays with a common endpoint the common endpoint is called the
vertex the two rays are called the sides of the
angle
![Page 16: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/16.jpg)
Angle
when naming an angle, the letter designating the vertex should always stand between two other letters.
an angle can also be named by using a single letter designating the vertex
A
B
C
![Page 17: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/17.jpg)
Angle
angles are measured in units called degrees (o)
a protractor is used to measure angles
![Page 18: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/18.jpg)
KINDS OF ANGLES ACCORDING TO MEASUREMENT
![Page 19: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/19.jpg)
RIGHT ANGLE
![Page 20: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/20.jpg)
Right Angle
an angle whose measure is 90o
a small square is usually placed to indicate a right angle
![Page 21: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/21.jpg)
Right Angle
E
D F
![Page 22: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/22.jpg)
ACUTE ANGLE
![Page 23: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/23.jpg)
an angle whose measure is greater than 0o and less than 90o
Acute Angle
![Page 24: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/24.jpg)
Acute Angle
H
G I
![Page 25: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/25.jpg)
OBTUSE ANGLE
![Page 26: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/26.jpg)
Obtuse Angle
an angle whose measure is greater than 90o but less than 180o
![Page 27: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/27.jpg)
Obtuse Angle
K
J L
![Page 28: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/28.jpg)
Try this!
![Page 29: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/29.jpg)
1.) 2
Use the figure to answer each questions below.
What kind of angle is each? Write A for Acute, R for Right and O for Obtuse.
12 3
4A
B CD
E
2.) 4
3.) 1 + 2
4.) 2 + 3
5.) 2 + 3 + 4
6.) 1 + 2 + 3
![Page 30: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/30.jpg)
![Page 31: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/31.jpg)
A1
![Page 32: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/32.jpg)
A2
![Page 33: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/33.jpg)
R3
![Page 34: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/34.jpg)
O4
![Page 35: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/35.jpg)
O5
![Page 36: Introduction to Geometry and Measurements](https://reader037.vdocuments.us/reader037/viewer/2022102806/5578396dd8b42a1f5b8b496b/html5/thumbnails/36.jpg)
O6