{"id":3297,"date":"2023-10-04T14:01:14","date_gmt":"2023-10-04T14:01:14","guid":{"rendered":"http:\/\/localhost\/ecole9ja\/?p=3297"},"modified":"2023-10-04T14:01:39","modified_gmt":"2023-10-04T14:01:39","slug":"week-10-and-11-ss2-second-term-mathematics-notes","status":"publish","type":"post","link":"https:\/\/ecolebooks.com\/nigeria\/posts\/week-10-and-11-ss2-second-term-mathematics-notes\/","title":{"rendered":"Week 10 and 11 – SS2 Second Term Mathematics Notes"},"content":{"rendered":"

\u00a0WEEK 10
\n SOLVING PROBLEM ON CIRCLE THEOREM.
\n<\/strong>ANGLES AT THE CNTRE OF A CIRCLE
\n<\/strong>THEOREM 1
\n<\/strong>The angle which an arc of a circle subtends at the centre of a circle is twice that which it subtends at any point on the circumference of the circle.
\n\"\"\/
\n\t\t\"\"\/\"\"\/\"\"\/\"\"\/
\n\t\t\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/
\n\t\t\"\"\/
\n\t\t\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\u00a0\u00a0\u00a0\u00a0<\/p>\n

\u00a0
\n\u00a0
\n\u00a0\"\"\/Given: A circle PQR, centre O.
\nTo prove that P \u00d4 Q = 2 P R Q
\nConstruction: Join RO, and extend to any point T.
\nProof: Po =Ro= Qo (radii)
\na = a1<\/sub> (base <s of Isos. POR)
\n P \u00d4 Q = a + a1<\/sub> = 2a (end <s of POR)
\n\"\"\/But P \u00d4 T + Q \u00d4 T
\nReflex of P \u00d4 Q = 2a + 2b = 2(a +b) = 2 PRQ
\n angle at centre = 2 x (at circum. Of a circle).
\nCorollary
\n<\/strong>The angle is a semi circle is a right angle
\n\"\"\/Given: A semi circle3 P Q R, Centre O.<\/p>\n

\u00a0
\n\u00a0\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/<\/p>\n

\u00a0
\n\u00a0
\n\u00a0\"\"\/
\n\t\t\"\"\/
\n\t\tTo prove that: PRO = 900<\/sup>
\n\t\tConstruction: None
\nProof: PQ is a diameter (given)
\n P \u00d4 Q = 1800<\/sup>
\n\t\t\t\"\"\/(< at centre = twice <s in circumference)
\n\"\"\/ 2PRO = 180o<\/sup>
\n\t\tHence PRO = = 900<\/sup> as required.<\/p>\n

\u00a0
\n\u00a0
\n\u00a0
\n\u00a0
\n\u00a0
\n\u00a0
\n\u00a0
\n\u00a0
\n\u00a0
\n\u00a0Theorem 2
\n<\/strong>
\n\u00a0\"\"\/Angles in the same segment of a circle and equal
\n\"\"\/\"\"\/\"\"\/
\n\t\t\"\"\/
\n\t\t\"\"\/\"\"\/\"\"\/
\n\t\t\"\"\/\"\"\/
\n\t\t\"\"\/\"\"\/<\/p>\n

\u00a0\"\"\/
\n\t\t\"\"\/<\/p>\n

\u00a0\"\"\/\"\"\/\"\"\/Given: points on a circle ABCD, AB is an arc of the circle.
\nTo prove that: AD B = AC B
\nConstruction: Join D and C to A and B, as shown above
\nProof: A \u00d4 B = 2(x1<\/sub> + x2<\/sub>)
\n\"\"\/\"\"\/X1<\/sub> = (A \u00d4 B)
\nA D B = A C B as required.<\/p>\n

\u00a0Assignment: page 117 exercise E Number 1<\/p>\n

\u00a0 WEEK ELEVEN
\n<\/strong>
\n\u00a0Cyclic Quadrilaterals
\n<\/strong>A cyclic quadrilateral is a four-sided figure whose vertices lie in side and touch the circumference of the circle. The opposite angles of C Cyclic quadrilateral lie in the opposite segment of the circle
\nTheorem 3
\n<\/strong>Opposite angles of a cyclic quadrilateral are supplementary.
\nGiven: A cyclic quadrilateral PQRS
\n\"\"\/\"\"\/To prove that: P Q R + P S R = 180o<\/sup>
\n\t\t\"\"\/\"\"\/Construction: Join PO and RO of the circle.
\n\"\"\/\"\"\/
\n\t\t\"\"\/
\n\t\t\"\"\/
\n\t\t\"\"\/\"\"\/\"\"\/
\n\t\t\"\"\/
\n\t\t\"\"\/
\n\t\t\"\"\/<\/p>\n

\u00a0\"\"\/<\/p>\n

\u00a0Proof; P \u00d4 R = 2y (< at Centre = twice on the circumf.)
\n\t\t 2x + 2y = 360o<\/sup> (<s at a point)
\n2(x +y) = 360o<\/sup>
\n\t\t\"\"\/X + y = 180o<\/sup>
\n\t\tP \u00d4R + PSR = 180o <\/sup><\/p>\n

\u00a0Assignment
\n<\/strong>Prove that if a straight line touches a circle a circle at a point, and from the point of contact a chord is drawn then the acute angles which this chord makes with the tangents are equal to the angle in the alternate segment.<\/p>\n

    \n
  1. Page 132 number 17 – 20\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

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