Mathematics Grade 9 8 Angles related to straight

Mathematics Grade 9 8 - Angles related to straight lines and parallel lines

Different types of angles 01. Adjacent angles 02. Complementary angles R • • • A A D C p 40 50 C B • • • Have a common vertex B Have a common arm BD Two angles ABD and DBC lie on opposite sides of the common arm BD • Is called as Adjacent angles B Q *If the sum of a pair of angles is 90 , They are a pair of complementary angles ABC + PQR =40 + 50=90 Complementary adjacent angles

03. Supplementary angles 04. Vertically opposite angles D A O B C If the sum of a pair of angles is 180, they are called as a pair of supplementary angles Straight lines AB and CD are intersected at O. Then AOC and DOB AOD and COB are vertically opposite angles And they are equal in magnitude Supplementary adjacent angles

Angles related to straight lines a + b = 180 Theorem 1; The sum of the adjacent angles formed by a straight line meeting another straight line Is two right angles According to theorem, 45 + 39 + b + 24= 180 Find the value of b

Theorem 2; The vertically opposite angles formed by the intersection of two straight lines are equal Formal proof of theorem D A Data O B C : the straight lines AB and CD are intersected at O To be proved: angle AOC and angle DOB and angle AOD and angle COB Proof : AOC + BOC = 180 ( Since AB is a straight line) AOC + AOD = 180 ( Since CD is a straight line) so AOC + BOC = AOC + AOD subtracting AOC from both sides, AOC + BOC – AOC = AOC + AOD – AOC BOC = AOD Similarly, AOC = BOD Do the exercises 8. 1 and 8. 2

E A Ga b d c B transversal C e Hf h g D F If two or more straight lines intersect by a straight line that line is called as Transversal. form, • Corresponding angles , • Alternate angles and • Allied angles let’s learn these types of angles…. .

According to the above diagram corresponding angles are a & e b & f c & g d & h, Alternate angles are c&e d & f, Allied angles are c&f d&e

Theorem; When a transversal intersects a pair of parallel lines, • The corresponding angles are equal • The alternate angles are equal • The sum of each pair of allied angles formed , equals to two right angles. 120 60 Corresponding angles Alternate angles Allied angles Complete the exercises 8. 3 & 8. 4 given in your text book Champika samarasinghe – Teacher Taxila Central college