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Mathematics 8 Online
OpenStudy (highschoolmom2010):

find missing legnth

OpenStudy (highschoolmom2010):

ganeshie8 (ganeshie8):

its a kite !

OpenStudy (highschoolmom2010):

well i know that

OpenStudy (highschoolmom2010):

i thought that would make DG the same length bc they are opposites

ganeshie8 (ganeshie8):

in kite, "nonvertex angles" are congruent, and the sides opposite them also congruent.

ganeshie8 (ganeshie8):

F and D are nonvertex angles here

ganeshie8 (ganeshie8):

that gives, EF = DE, and FG = GD

OpenStudy (highschoolmom2010):

oh...

ganeshie8 (ganeshie8):

im sure u didnt get this clearly enough

OpenStudy (highschoolmom2010):

so the answer was B bc DE and EF are equal right?

ganeshie8 (ganeshie8):

Yes answer is EF = 6 = DE

OpenStudy (highschoolmom2010):

i really appreciate you explaining it to me :)

ganeshie8 (ganeshie8):

np :)

ganeshie8 (ganeshie8):

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ganeshie8 (ganeshie8):

the sides opposite to the diagonal thats bisected are congruent

ganeshie8 (ganeshie8):

there is another simple way to see this, without using kite. using oly the triangles if you're up for it :)

OpenStudy (highschoolmom2010):

sure

ganeshie8 (ganeshie8):

ganeshie8 (ganeshie8):

look at the pic, lets say, the diagonals are intersecting at O

ganeshie8 (ganeshie8):

the two small triangles OFE and ODE are congruent by HL theorem. so by CPCTC, FE = DE. Done.

OpenStudy (highschoolmom2010):

CPCTC what is that

ganeshie8 (ganeshie8):

its aan acronym

ganeshie8 (ganeshie8):

CPCTC = Corresponding Parts of Congruent Triangles are Congruent

OpenStudy (highschoolmom2010):

oh ok that makes sense

ganeshie8 (ganeshie8):

it simply says this : when two triangles are congruent, then their corresponding parts are congruent

ganeshie8 (ganeshie8):

great :)

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