LINES AND ANGLES

CAN YOU DRAW A LINE SEGMENT

I EXTENDED INDEFINETLY ON BOTH SIDES DIFFERENTIATE BETWEEN A LINE AND LINE SEGMENT I AM MADE UP OF POINTS. I HAVE TWO END POINTS. I HAVE DEFINETE LENGTH I AM MADE UP POINTS . I HAVE NO END POINTS, I EXTENDED INDEFINETLY ON BOTH SIDES LINE LINE SEGMENT

ANGLES TWO RAYS WITH A COMMON END POINTS FORM AN ANGLIE TWO RAYS ARE THE ARMS OF THE ANGLE. COMMON ENDPOINT IS THE VERTEX OF THE ANGLE

There are four main types of angles. Right angle Acute angle Obtuse angle A B C A B C A B C Straight angle B A C

Acute angle: An angle whose measure is less than 90 degrees.

Examples Of Acute Angle

Right angle: An angle whose measure is 90 degrees.

Examples Of Right Angle

Obtuse angle: An angle whose measure is greater than 90 degrees.

Examples Of Obtuse Angle

Straight angle: An angle whose measure is 180 degrees.

Examples Of Straight Angle

Vertically opposite angles Complimentary angles Pairs Of Angles : Types Adjacent angles Vertically opposite angles Complimentary angles Supplementary angles Linear pairs of angles

Adjacent Angles ABC and DEF are not adjacent angles Two angles that have a common vertex and a common ray are called adjacent angles. C D B A Common ray Common vertex D E F A B C Adjacent Angles ABD and DBC ABC and DEF are not adjacent angles Adjacent angles do not overlap each other.

Adjacent angles are “side by side” and share a common ray. 15º 45º

These are examples of adjacent angles. 45º 80º 35º 55º 130º 50º 85º 20º

These angles are NOT adjacent. 100º 50º 35º 35º 55º 45º

ÐABC and ÐDEF are complimentary because Complimentary Angles If the sum of two angles is 900, then they are called complimentary angles. 600 A B C 300 D E F ÐABC and ÐDEF are complimentary because ÐABC + ÐDEF 600 + 300 = 900

ÐDEF and ÐPQR are not complimentary because Contd…. If the sum of two angles is more than 900 or less than 900, then they not complimentary angles. 700 D E F 300 p Q R ÐDEF and ÐPQR are not complimentary because ÐDEF + ÐPQR 700 + 300 = 1000

ÐPQR and ÐABC are supplementary, because Supplementary Angles If the sum of two angles is 1800 then they are called supplementary angles. R Q P A B C 1000 800 ÐPQR and ÐABC are supplementary, because ÐPQR + ÐABC 1000 + 800 = 1800

ÐDEF and ÐPQR are not supplementary because Contd…. If the sum of two angles is more than 1800 or less than 1800, then they are not supplementary angles. C B A 1100 D E F 800 ÐDEF and ÐPQR are not supplementary because ÐABC + ÐDEF 1100 + 800 = 1900

Two adjacent supplementary angles are called linear pair of angles. 1200 600 C D P ÐAPC + ÐAPD 600 + 1200 = 1800

VERTICALLY OPPOSITE ANGLES ARE EQUAL WHEN TWO LINES INTERSECT THEY MAKE TWO PAIRS OF VERTICALLY OPPOSITE ANGLES 75º 105º VERTICALLY OPPOSITE ANGLES ARE OPPOSITE TO ONE ANOTHER VERTICALLY OPPOSITE ANGLES ARE EQUAL

Adjacent angles: ÐAPC and ÐCPD Name the vertically opposite angles and adjacent angles in the given figure: A D B C P Vertically opposite angles: ÐAPC and ÐBPD Adjacent angles: ÐAPC and ÐCPD ÐAPB and ÐCPD ÐAPB and ÐBPD

Directions: Identify each pair of angles as vertical, supplementary, complementary, or none of the above.

#1 120º 60º

#1 120º 60º Supplementary Angles

#2 60º 30º

#2 60º 30º Complementary Angles

#3 75º 75º

#3 Vertical Angles 75º 75º

#4 60º 40º

#4 60º 40º None of the above

#5 60º 60º

#5 60º 60º Vertical Angles

#6 135º 45º

#6 135º 45º Supplementary Angles

#7 25º 65º

#7 25º 65º Complementary Angles

#8 90º 50º

#8 90º 50º None of the above

Directions: Determine the missing angle.

#1 ?º 45º

#1 135º 45º

#2 ?º 65º

#2 25º 65º

#3 ?º 35º

#3 35º 35º

#4 ?º 50º

#4 130º 50º

#5 ?º 140º

#5 140º 140º

#6 ?º 40º

#6 50º 40º