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Geometry Journal 4

Geometry Journal 4. Michelle Habie 9-3. Triangles :. Sides : Scalene ( 3 sides are different ) Equilateral ( 3 sides are thesame ) Issoceles ( 2 sides are equaland 1 isdifferent ) Angles : Acute ( 3 anglesmeasurelessthan 90° ) Right ( 1 anglemeasures 90° )

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Geometry Journal 4

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  1. Geometry Journal 4 Michelle Habie 9-3

  2. Triangles: Sides: Scalene (3 sides are different) Equilateral (3 sides are thesame) Issoceles (2 sides are equaland 1 isdifferent) Angles: Acute (3 anglesmeasurelessthan 90°) Right (1 anglemeasures 90°) Obtuse(1 anglesmeasuresgreaterthan 90°) We use eachtype of triangleaccordingtoitssides and itsanglemeasurementbecauseeach of them, has differentproperties and uses.

  3. Examples: IssocelesTriangle Obtuse–roofof a house. RightTriangletomeasuretheshape of thebuilding. Equilateral- tobuildgamesmadeof iron. Scalene

  4. Partsof a Triangle: 1 angle Hyoptenuse Parts: 3 sides 3 interior angles 1 exterior angleforeachside Hypotenuse The exterior angleisformedbytheextension of oneside of thetriangle. The exterior angle has two remote interior angleswhichare non-adjacenttotheexterior one. An interior angleisformedwhentwosides of a trianglemeet. TriangleSumTheorem: Itstatesthatthesum of the3 interior angles of anytrianglehavetobeequalto180 degrees. 1 side 1 side 1 angle 1 angle 1 side

  5. Ang. A+ Ang. B+ aNG. C =180 X+19+2x+1+100=180 3x+120=180 3x=60 X=20 Examples: Interior: 3x+5 B A 118 5x+1 B 2x+3 X+19 100 99 3x+5+2x+13=118 5x+18=118 5x=100 X=20 C X+8 A 2x+1 5x++x+8=99 6x+9=99 6x=90 x=15 Exterior: 3x-10 2z+1 2 10 6z-9 4 X+15 3 25 1

  6. Exterior AngleTheorem: Statesthattheexterior angleisthesameas thesum of thetworemote interior angles. How can it be used? It can be used in navigationtofindanglesbyknowingtwo and findthe target ortheplace they are leadingto.

  7. Congruence: Congruenceforshapesmeansthattheobjectshavethesameshapeandthesamemeasurementswhilecorresponding in shapesmeanssidesthatocupythesameposition. Whileprovingtwotriangles are congruentyou may needgoprovethecorrespondingsidesorangles are congruentandthenjumpinto a conclusionthatthetwotriangles are congurent by the CPCTC. MeaningthattheCongruentPartsoftheCongruentTriangles are alwayscongruent.

  8. CPCT Examples: 4cm 10cm 8cm 8cm 8cm 8cm 13 cm 4cm 13 cm 8cm 8cm 10cm 6cm 13cm 15 cm 15 cm 13cm 6cm

  9. SSS Postulate: Ifthreesides of onetriangleare congruenttothreesides of anothertriangle, thethetrianglesare congruent.

  10. Examples: 16cm 9cm 9cm 9cm 9cm 16cm 5cm 5cm 24 cm 16cm 16cm

  11. SAS Postulate: Thistype of postulateisusedtoprovethattwotrianglesare congruent. Thispostulatesaysthatiftwosides of onetriangle and theincludedangle of it, and congruent=nottothecorrespondingtwosides and theincludedangle of thesecondtriangles, thanthetwofigures are congruent.

  12. Examples: 1. V C E Y U D F A X Z W B ABC congruent EFD XYZ congruent UVW 1 4 2 6 3 5 123 congruent 456

  13. ASA Postulate: Iftwoangles and theincludedside of onetriangleare congruenttotwoangles and theincludedside of anothertriangle, thenthetrainglesare congruent.

  14. Examples: 25 25 32 76 100 32 100 25 25 90 90 76 30 27 15 30 15 27

  15. AAS Theorem: Iftwoangles and a non includedside of onetriangleare congruenttothecorrespondingangles and non includedside of anothertriangle, thenthetrianglesare congruent.

  16. Examples: = angle 30 30 75 75 8in 8in 14 21 9 cm 9 cm 21 14

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