Form 2 Mathematics – CONGRUENCE OF SIMPLE POLYGON msomimaktaba, November 13, 2018August 17, 2024 CONGRUENCE OF SIMPLE POLYGON The triangles above are drawn such thatCB= ZYAC=XZB=YXCorresponding sides in the triangles are those sides which are opposite to the equal angles i.e.If the corresponding sides are equal i.e.In general, polygons are congruent if corresponding sides and corresponding angles are equal. The symbol for congruence is Congruence of triangles Case 1: Given three sidesTwo triangles are congruent if the three pairs of corresponding sides are such that the sides in each pair are equal.Consider the triangles below:Note: SSS- is an abbreviation of side- side- sideExamples : Solution Construction of A is joined C Construction; A joined to DCase 2; Given two sides and the included angle (SAS) Two triangles are congruent if two pairs of corresponding sides are such that the sides in each pair are equal and the angles included between the given sides in each triangle are equal.ExamplesCase 3; Given two angles and a corresponding side Two triangles are congruent if two pairs of corresponding angles are such that the angles in each triangle are equal.ExampleSolution Case 4: Given that a right angle hypotenuse and one side (RHS)The right angled triangles are congruent if the hypotenuse and a side of one triangle are respectively equal to the hypotenuse and side of another triangleExample: Use the figure below to prove thatSolutionAC= AB -right anglesThereforeNote:R.H.S – Right angle hypotenuse sideIsosceles triangle theorem The base angles of an isosceles triangle are equalConstruction:-Exercise 1.SolutionABCD = Common line They are alternate interior angle AB=CD givenBC =AD given SOLUTION6. O is the center of the circle ABCD, if AC and BD and diameter of the circle and the line segments AD, AB and CB are drawn prove that Solution CONVERSE THE ISOSCELES TRIANGLE THEOREM If two angles of a triangle are equal then sides opposite those angles are equal Given that C=Required to prove = Construction A and D are joined such that THEOREMS OF PARALLELOGRAMS1) The opposite sides of the parallelogram are equalGiven a parallelogram ABCDRequired to proveConstruction:D is formed to BAB= CD -is interior angles AB//DCAD= BC -is interior angles AB//DCTherefore2. The opposite angles of the parallelogram are equal DB= DBAC + DB=180Interior angle of the same side of // AC + DB=180º interior angles on side of //ThereforeSimilarlyDB + AC=180º interior angles the same side of //BD + AC=180º interior angles the same side of ,// ThereforeDB + ABC= BD + ACDB= BDHence opposite angles of a parallelogram are equal.3.The diagonals of a parallelogram bisect each other 4. The diagonals of a parallelogram intersect each otherIf one pair of the opposite sides of a quadrilateral are equal and parallel then the other pair of the opposite side are equal and parallel.Example ALL NOTES FOR ALL SUBJECTS QUICK LINKS:AGRICULTURE O LEVEL PURE MATHEMATICS A LEVELBAM NOTES A LEVELBASIC MATH O LEVELBIOLOGY O/A LEVELBOOK KEEPING O LEVELCHEMISTRY O/A LEVELCIVICS O LEVELCOMPUTER(ICT) O/A LEVELECONOMICS A LEVELENGLISH O/A LEVELCOMMERCE O/A LEVELACCOUNTING A LEVELGENERAL STUDIES NOTESGEOGRAPGY O/A LEVELHISTORY O/A LEVELKISWAHILI O/A LEVELPHYSICS O/A LEVELMOCK EXAMINATION PAPERSNECTA PAST PAPERS Basic Mathematics Study Notes Form 2 Basic Mathematics Study Notes Msomi Maktaba All Notes FORM 2MATHEMATICSPost navigationPrevious postNext postRelated Posts Form 3 Kiswahili Study Notes Form 3 Kiswahili – UTUNGAJI WA KAZI ZA FASIHI ANDISHI November 13, 2018February 13, 2019ALL NOTES FOR ALL SUBJECTS QUICK LINKS: AGRICULTURE O LEVEL PURE MATHEMATICS A LEVEL BAM NOTES A LEVEL BASIC MATH O LEVEL BIOLOGY O/A LEVEL BOOK KEEPING O LEVEL CHEMISTRY O/A LEVEL CIVICS O LEVEL COMPUTER(ICT) O/A LEVEL ECONOMICS A LEVEL ENGLISH O/A LEVEL COMMERCE O/A LEVEL ACCOUNTING A LEVEL… Read More Form 5 General Studies (GS) Study Notes Form 5 General Studies (GS) – SCIENCE AND TECHNOLOGY IN DEVELOPMENT November 7, 2018February 13, 2019Definition of the terms science and technology Science is an organized body of knowledge derived from a systematic observation and experiment of natural condition. Science involves the extract of knowledge and skills on something through testing, smelling, touching and experiments for the sake of deriving principles and laws guiding the… Read More English Study Notes LITERATURE FORM 1 – WRITING PERSONAL LETTER November 11, 2018February 13, 2019 Friendly letters Use to express your thought and feelings to get something done both the content and the form of a letter say something for you and about you. The content is what you write in a letter, form is how it look There are two… Read More Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment *Name * Email * Website Save my name, email, and website in this browser for the next time I comment. Δ
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