1-3 slide show - measuring segments...2018/05/01 · measuring segments •a line segmentis a set...
TRANSCRIPT
MeasuringSegments
Unit1Lesson3
MeasuringSegments
Studentswillbeableto:
•Findthemeasureofsegmentsusingtherulerpostulate,thedefinitionofcongruentsegments,midpointsandthesegment
additionpostulate.• Findthelengthandmidpointofasegment.• Understandthecongruencyofsegments.
.
MeasuringSegments
KeyVocabulary:LineSegmentDistance/length
CongruentsegmentsSegmentbisectorSegmentpartition
.
MeasuringSegments
• Alinesegment isasetofpointsandhasaspecificlengthi.e.itdoesnotextendindefinitely.• Alinesegmentisnamedbytwopointsonthelinesegmentwithalinesegmentsymbolabovetheletters.• Thelinesegmentalwayshasacertainlengththatcanbemeasuredusingaruler.
MeasuringSegments
RulerPostulate• Everypointonalinecanbepairedwitharealnumber.Thismakesaone-to-onecorrespondencebetweenthepointsonthelineandtherealnumbers.• Therealnumberthatcorrespondstoapointiscalledthecoordinateofthepoint.
MeasuringSegments
SampleProblem1: Findthelengthofeachsegmentusingaruler.a.
𝑨𝑩
𝑨𝑩 =?
MeasuringSegments
SampleProblem1: Findthelengthofeachsegmentusingaruler.a.
𝑨𝑩
𝑨𝑩 =?
𝑨𝑩 = 𝐴𝑐𝑡𝑢𝑎𝑙𝑙𝑒𝑛𝑔𝑡ℎ𝑓𝑟𝑜𝑚𝑦𝑜𝑢𝑟𝑟𝑢𝑙𝑒𝑟
MeasuringSegments
SampleProblem1: Findthelengthofeachsegmentusingaruler.b.
𝑻
𝑻𝑷 =?𝑷
MeasuringSegments
SampleProblem1: Findthelengthofeachsegmentusingaruler.b.
𝑻
𝑻𝑷 =?
𝑻𝑷 = 𝐴𝑐𝑡𝑢𝑎𝑙𝑙𝑒𝑛𝑔𝑡ℎ𝑓𝑟𝑜𝑚𝑦𝑜𝑢𝑟𝑟𝑢𝑙𝑒𝑟
𝑷
MeasuringSegments
SampleProblem1: Findthelengthofeachsegmentusingaruler.c.
𝑹
𝑹𝑫 =?
𝑫
MeasuringSegments
SampleProblem1: Findthelengthofeachsegmentusingaruler.c.
𝑹
𝑹𝑫 =?
𝑹𝑫 = 𝐴𝑐𝑡𝑢𝑎𝑙𝑙𝑒𝑛𝑔𝑡ℎ𝑓𝑟𝑜𝑚𝑦𝑜𝑢𝑟𝑟𝑢𝑙𝑒𝑟
𝑫
MeasuringSegments
Findingthelengthoflinesegmentusingnumberline• Thedistancebetweenpointsonnumberlinerepresentthelengthoflinesegment.• Thedistancebetweenanytwopointsistheabsolutevalueofthedifferenceofthecoordinates.Ifthecoordinatesofpoints𝑨 and𝑩 are𝒂 and𝒃,thenthedistancebetween𝑨 and𝑩 is:𝑨𝑩 = 𝒂 − 𝒃 or𝑨𝑩 = 𝒃 − 𝒂• Twolinesegmentshavingsamelengthsaresaidtobecongruentlinesegments.
MeasuringSegments
SampleProblem2: Findthelengthofeachsegmentusingnumberline.Determinewhichsegmentsarecongruent.a. 𝑨𝑪 =? 𝑪𝑷 =? 𝑯𝑳 =? 𝑨𝑳 =?
0 1 2 3 4-1-2-3-4 5 6-5-6
𝑨𝑪𝑯𝑷𝑳
MeasuringSegments
SampleProblem2: Findthelengthofeachsegmentusingnumberline.Determinewhichsegmentsarecongruent.a. 𝑨𝑪 =? 𝑪𝑷 =? 𝑯𝑳 =? 𝑨𝑳 =?
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𝑨𝑪𝑯𝑷𝑳
𝑨𝑪 = −𝟓 − −𝟐 = −𝟓 + 𝟐 = −𝟑 = 𝟑𝑪𝑷 = −𝟐 − 𝟒 = −𝟔 = 𝟔𝑯𝑳 = 𝟐 − 𝟓 = −𝟑 = 𝟑𝑨𝑳 = −𝟓 − 𝟓 = −𝟏𝟎 = 𝟏𝟎
𝑨𝑪 ≅ 𝑯𝑳𝑨𝑪 = 𝑯𝑳
MeasuringSegments
SampleProblem2: Findthelengthofeachsegmentusingnumberline.Determinewhichsegmentsarecongruent.b. 𝑱𝑼 =? 𝑹𝑻 =? 𝑮𝑹 =? 𝑭𝑻 =?
0 1 2 3 4-1-2-3-4 5 6-5-6
𝑹𝑮𝑻𝑭𝑼𝑱
MeasuringSegments
SampleProblem2: Findthelengthofeachsegmentusingnumberline.Determinewhichsegmentsarecongruent.b. 𝑱𝑼 =? 𝑹𝑻 =? 𝑮𝑹 =? 𝑭𝑻 =?
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𝑹𝑮𝑻𝑭𝑼𝑱
𝑱𝑼 = 𝟓 − 𝟑 = 𝟐 = 𝟐𝑹𝑻 = −𝟔 − (−𝟏) = −𝟔 + 𝟏 = −𝟓 = 𝟓𝑮𝑹 = −𝟒 − (−𝟔) = −𝟒 + 𝟔 = 𝟐 = 𝟐𝑭𝑻 = 𝟐 − (−𝟏) = 𝟐 + 𝟏 = 𝟑 = 𝟑 𝑱𝑼 ≅ 𝑮𝑹
𝑱𝑼 = 𝑮𝑹
MeasuringSegments
SegmentAdditionPostulate:
Ifthreepoints𝑨,𝑩,and𝑪 arecollinearand𝑩 isbetween𝑨 and𝑪,thenthedistance𝑨𝑪 isthesumofdistance𝑨𝑩 and𝑩𝑪.
𝑨𝑩 + 𝑩𝑪 = 𝑨𝑪
MeasuringSegments
SampleProblem3: Findthelengthofeachsegmentusingsegmentadditionpostulate.Drawadiagramtorepresentthesituation.a.Point𝒁 isbetweenpoints𝑻 and𝑪.Thepointsarecollinear. 𝐓𝐙 = 𝟑𝒄𝒎𝒁𝑪 = 𝟏𝟐𝒄𝒎𝑻𝑪 =?
MeasuringSegments
SampleProblem3: Findthelengthofeachsegmentusingsegmentadditionpostulate.Drawadiagramtorepresentthesituation.a.Point𝒁 isbetweenpoints𝑻 and𝑪.Thepointsarecollinear. 𝐓𝐙 = 𝟑𝒄𝒎𝒁𝑪 = 𝟏𝟐𝒄𝒎𝑻𝑪 =?𝑻𝒁𝑪
𝟑𝒄𝒎𝟏𝟐𝒄𝒎
𝑻𝑪 = 𝑻𝒁 + 𝒁𝑪𝑻𝑪 = 𝟑𝒄𝒎 + 𝟏𝟐𝒄𝒎 = 𝟏𝟓𝒄𝒎𝑻𝑪 = 𝟏𝟓𝒄𝒎
MeasuringSegments
SampleProblem3: Findthelengthofeachsegmentusingsegmentadditionpostulate.Drawadiagramtorepresentthesituation.b.Point𝑺 isbetweenpoints𝑸 and𝑲.Thepointsarecollinear. 𝑸𝑲 = 𝟐𝟒𝒄𝒎𝑸𝑪 = 𝟏𝟎𝒄𝒎𝑺𝑲=?
MeasuringSegments
SampleProblem3: Findthelengthofeachsegmentusingsegmentadditionpostulate.Drawadiagramtorepresentthesituation.b.Point𝑺 isbetweenpoints𝑸 and𝑲.Thepointsarecollinear.𝑸𝑲 = 𝟐𝟒𝒄𝒎𝑸𝑪 = 𝟏𝟎𝒄𝒎𝑺𝑲=?
𝑸𝑺𝑲𝟐𝟒𝒄𝒎
𝟏𝟎𝒄𝒎
𝑸𝑲 = 𝑸𝑺 + 𝑺𝑲𝑺𝑲 = 𝑸𝑲−𝑸𝑺𝑺𝑲 = 𝟐𝟒𝒄𝒎 − 𝟏𝟎𝒄𝒎 = 𝟏𝟒𝒄𝒎𝑺𝑲 = 𝟏𝟒𝒄𝒎
MeasuringSegments
• Themidpoint isthemiddlepointofalinesegment.Itisequidistantfrombothendpoints,anditisthecentroidbothofthesegmentandoftheendpoints.• Themidpointofasegment,dividesthesegmentintotwocongruentsegments.• Asegmentbisector isapoint,lineoralinesegmentthatpassesthroughamidpointofanothersegment.• Asegmentbisectorisusuallyatthecenterofthelinesegmentandalwaysincludesthemidpointofthelinesegment.
MeasuringSegments
𝒉
𝒉isasegmentbisectorof𝑨𝑪𝑩isamidpointof𝑨𝑪
𝑨𝑩𝑪
MeasuringSegments
SampleProblem4: Findthelengthofeachsegment.Drawadiagramtorepresentthesituation.a. Point𝑩 ismidpointofsegment𝑴𝑵.𝑴𝑵 = 𝟏𝟎𝒄𝒎𝑴𝑩 =?𝑩𝑵 =?
MeasuringSegments
SampleProblem4: Findthelengthofeachsegment.Drawadiagramtorepresentthesituation.a. Point𝑩 ismidpointofsegment𝑴𝑵.𝑴𝑵 = 𝟏𝟎𝒄𝒎𝑴𝑩 =?𝑩𝑵 =?
𝑴𝑩𝑵
𝟏𝟎𝒄𝒎
MeasuringSegments
SampleProblem4: Findthelengthofeachsegment.Drawadiagramtorepresentthesituation.a. Point𝑩 ismidpointofsegment𝑴𝑵.𝑴𝑵 = 𝟏𝟎𝒄𝒎𝑴𝑩 =?𝑩𝑵 =?
𝑴𝑵 = 𝑴𝑩 + 𝑩𝑵𝑴𝑩 = 𝑩𝑵𝑴𝑵 = 𝟐 ∗𝑴𝑩
𝑴𝑩 =𝑴𝑵𝟐 =
𝟏𝟎𝒄𝒎𝟐 = 𝟓𝒄𝒎 𝑩𝑵 = 𝟓𝒄𝒎
𝑴𝑩 = 𝑩𝑵
MeasuringSegments
SampleProblem4: Findthelengthofeachsegment.Drawadiagramtorepresentthesituation.b. Point𝑫 ismidpointofsegment𝑭𝑻.𝑭𝑫 = 𝟔𝒊𝒏.𝑫𝑻 =?𝑭𝑻 =?
MeasuringSegments
SampleProblem4: Findthelengthofeachsegment.Drawadiagramtorepresentthesituation.b. Point𝑫 ismidpointofsegment𝑭𝑻.𝑭𝑫 = 𝟔𝒊𝒏.𝑫𝑻 =?𝑭𝑻 =?
𝑭𝑫𝑻
𝟔𝒊𝒏.
MeasuringSegments
SampleProblem4: Findthelengthofeachsegment.Drawadiagramtorepresentthesituation.b. Point𝑫 ismidpointofsegment𝑭𝑻.𝑭𝑫 = 𝟔𝒊𝒏.𝑫𝑻 =?𝑭𝑻 =?
𝑭𝑫 = 𝑫𝑻𝑫𝑻 = 𝟔𝒊𝒏.
𝑭𝑻 = 𝑭𝑫 + 𝑫𝑻𝑭𝑻 = 𝟔𝒊𝒏. +𝟔𝒊𝒏. = 𝟏𝟐𝒊𝒏.𝑭𝑻 = 𝟏𝟐𝒊𝒏.
MeasuringSegments
SampleProblem5: Findthecoordinateofthemidpointofeachsegment.a.
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𝑹𝑩
MeasuringSegments
SampleProblem5: Findthecoordinateofthemidpointofeachsegment.a.
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𝑹𝑩
𝑴𝑹𝑩 =−𝟐 + 𝟐𝟐 =
𝟎𝟐
𝑴𝑹𝑩 = 𝟎 Thecoordinateofthemidpointof 𝑹𝑩is𝟎
MeasuringSegments
SampleProblem5: Findthecoordinateofthemidpointofeachsegment.b.
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𝑲𝑳
MeasuringSegments
SampleProblem5: Findthecoordinateofthemidpointofeachsegment.b.
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𝑲𝑳
𝑴𝑲𝑳 =−𝟑 + 𝟏𝟐 =
−𝟐𝟐
𝑴𝑲𝑳 = −𝟏Thecoordinateofthemidpointof𝑲𝑳is − 𝟏
MeasuringSegments
• Asegmentpartition isapoint,lineoralinesegmentthatpartitionsthelinesegmentinaparticularratio.• Iftheratioisequal,thesegmentpartitionbecomesasegmentbisector.
MeasuringSegments
SampleProblem6: Dividethelinesegmentintheratiogivenbyputtingadotatthepartition.a.
𝑽𝑩
𝑹𝒂𝒕𝒊𝒐𝟏: 𝟒
MeasuringSegments
SampleProblem6: Dividethelinesegmentintheratiogivenbyputtingadotatthepartition.a.
𝑽𝑩
𝑹𝒂𝒕𝒊𝒐𝟏: 𝟒
MeasuringSegments
SampleProblem6: Dividethelinesegmentintheratiogivenbyputtingadotatthepartition.b.
𝑯𝑳
𝑹𝒂𝒕𝒊𝒐𝟑: 𝟏
MeasuringSegments
SampleProblem6: Dividethelinesegmentintheratiogivenbyputtingadotatthepartition.b.
𝑯𝑳
𝑹𝒂𝒕𝒊𝒐𝟑: 𝟏