Form 2 Mathematics – SIMILARITY AND ENLARGEMENT msomimaktaba, November 13, 2018August 17, 2024 SIMILARITY AND ENLARGEMENTSimilar figures: Two polygons are said to be similar if they have the same shape but not necessarily the same size.When two figures are similar to each other the corresponding angles are equal and the ratios of corresponding sides are equal.SIMILARTRIANGLE Triangle are similar when their corresponding angles are equal or corresponding sides proportional consider the figure below : Since corresponding angles are equal then the two triangles are similarAlso: Since the ratio of corresponding sides are equal then the two triangles are similarNote () is a sign of similarity, from above ABC PQRExamples1. Given that SLKNFR, identify all the corresponding angles and corresponding sidesSolution: Corresponding sides; 3. One rectangle has length 10cm and width 5cm. The second rectangle has length 12cm and width 4cm. Are the two rectangles similar? ExplainSolution: Therefore; the two rectangles are not similar because the ratio of corresponding sides are not proportional4. A rectangle has length 16cm and width 23cm, A second rectangle has length 12cm and width 9cm. Are the two rectangles similar? Explain Solution: Therefore;The rectangles are not similar because the ratio of corresponding sides are not proportionalConditions for two triangles to be similar;1. Corresponding angles are equal or corresponding sides proportional For other polygons– Corresponding angles equal and corresponding sides proportionalQUESTIONS:a) Given that PQR LMN and that PQRABC identify the corresponding angles and sides between ABC and LMN.solutionExercise Solution: a) ABC = 70O ,MNL = 400 ,ACB =? a) Name the triangles which are similarb) Identify the corresponds anglesSolution:The triangles ABT and KLS are similar8. Name the triangles which are similar to ADC 10. Which of the following figures are always similar?a) circles d) Rhombusesb) Hexagons e) Rectanglesc) squares f) Congruent polygonsSolution:The figures which are always similara) circlesb) squaresExercise 1 M < AEF = 420M < AFE =?900 – 420 = 480M < AFE = 480 INTERCEPT THEOREM A line drawn parallel to one side of a triangle divides the other two sides in the same ratio AAA – Similarity theoremIf a correspondence between two triangles is such that two pairs of corresponding angles are equal then the two triangles are similar SSS – similarity TheoremIf the two triangles is such that corresponding sides are proportional, then the triangles are similarSAS – Similarities theoremIf the two triangles is such that two pairs of corresponding sides are proportional and the included angles are congruent then the triangles are similar PROPERTIES OF SIMILAR TRIANGLESFrom the previous discussion, properties of similar triangles can be summarized as:-1. Corresponding angles of similar triangles are equal2. Corresponding sides of similar triangles are similar3. Two triangles are similar if two triangles of one triangle are respectively equal to two corresponding angles of the other4. Two triangles are similar if an angle of one triangle equals an angle of other and the sides including these angles are proportional.ENLARGEMENTScale enlargementScale – is a ratio between measurements of a drawing to the actual measurement.It is normally started in the form 1: in example if a scale o a map is 1: 20000, then 1 unit on the map represents 20000 units on the groundScale = Examples of scales1. Find the length of the drawing that representsa) 1 stem when the scale is 1:500,000Solution:1:500,000 means 1 cm on the drawing represents 500,000 cm on the actual distance = 500,000x = 1500,000X = X = 3cmThe drawing length is 3cmb) 45km when scale is 1cm to 900mSolution:Scale = 1: 90000Scale = X = The drawing distance is 50cm2. Find the actual length represented bya) 3.5cm metres when the scale is 1: 5000mSolution:Scale = = y = 5000 x 3.5y = 17500cmy = = 175mThe distance is 175mb) 1.8mm when the scale is 1cm to 500metresSolution:Scale = = v= 0.18 x 50000v = 9000cmv = 90mThe actual length is 90mExercise:1. Find the length of the drawing that representsa) 200m when the scale is 1cm to 50metersScale = == X = 4cmThe length of drawing = 4cm b) 1.5 when the scale is 1cm to 100metres= x = 15cmThe length of drawing = 15cmd) 1600km when the scale is 1mm to 1km == x = 1600km The length of drawing is 1.6 mme) 10m when the scale is 1: 500= = x = 2cmThe length of drawing= 2cm2. Find the actual length represented bya) 13.15mm which the scale is 1: 4000Scale = =x = 0.0032875mmb) 3.78cm when the scale is 1mm to 50km = = x = 0.00000007563. On a scale drawing the length of a ship is 42cm. If the actual length of the ship is 84cm, what is a scale if width of the ship is 23cm, what is the corresponding width of the drawing?Solution:Scale = == x = 1:200Scale = 1:200== x = 11.5cmThe corresponding width of drawing = 11.5cm ENLARGEMENTWhen two figures are similar, one can be considered the enlargement of the other (a)b) Square ABCD is the enlargement of PQRSc)The larger circle is the enlargement of smaller circleExample 1. State whether ABCD is the enlargement of PQRS Solution:Since the correspond side are in the ratio 0f 2:1 and corresponding equal then ABCDPQRSScale factor:If two polygons are similar and the ratio of their corresponding sides is 5:3, then the enlargement scale is 5/3ExampleFind the scale of enlargement hence calculate Solution: Scale factor for areasIf two polygons have a scale factor of K then the ratio of the areas is K2ExampleIf ABSVST and the area of STV is 6 square cm. find the area of ABC Exercise1. Two triangle are similar but not congruent. Is one the enlargement of the others one triangle is the enlargement of the other2. The length of rectangle is twice the length of another rectangle. Is one necessary an enlargement of other. Explain? No, Since the width are not necessarily in the same proportional as the lengths.3. In figure below, show that PQR is not an enlargement of DEF = = , = = PQR is not enlargement of DEF5. Triangle XYZ is similar to triangle ABC and XY = 8cm. If the area or the triangle XYZ is 24cm2 and the area of the triangle ABC is 96cm2, calculate the length of AB. 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 Book Keeping Study Notes Form 3 Book Keeping – PROVISIONS November 12, 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 SFUCHAS selected applicants 2021/22 | St. Francis University College of Health and Allied Sciences selected applicants 2021/2022 February 4, 2024SFUCHAS Selected applicants 2023/2024 pdf: Have you applied for Diploma, certificate or bachelor degree admission at St. Francis University College of Health and Allied Sciences for 2023/2024 academic year and you have been anxiously waiting to see if you have been selected to join SFUCHAS and you don’t know how… Read More Msomi Maktaba All Notes 2024 Mapinduzi Cup Final Preview February 3, 2024Mapinduzi Cup Final: Matokeo Simba SC vs Mlandege – January 13, 2024 The much-anticipated Mapinduzi Cup Final on January 13, 2024, is set to feature a thrilling encounter between Simba SC and Mlandege. 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