- #1
Sirsh
- 267
- 10
Hello all, the picture i have attached is the question.
http://img842.imageshack.us/img842/8921/geometricproof.png
I've concluded that there are two i isosceles triangles in this one triangle.
[tex]\angle[/tex]PSQ + [tex]\angle[/tex]QSR = 90degrees
Finding the angle in one of the isosceles triangles.
[tex]\Delta[/tex]RQS with RQ = SQ
RQ = SQ (given)
If we put a line through the isosceles triangle and call this Z.
RZ = SZ
RZ = SZ (common to both)
therefore: [tex]\Delta[/tex]RZQ =~ [tex]\Delta[/tex]SZQ
therefore: [tex]\Delta[/tex]QRZ = [tex]\Delta[/tex]QSZ
which results in: [tex]\angle[/tex]QRS = [tex]\angle[/tex]QSR
http://img842.imageshack.us/img842/8921/geometricproof.png
I've concluded that there are two i isosceles triangles in this one triangle.
[tex]\angle[/tex]PSQ + [tex]\angle[/tex]QSR = 90degrees
Finding the angle in one of the isosceles triangles.
[tex]\Delta[/tex]RQS with RQ = SQ
RQ = SQ (given)
If we put a line through the isosceles triangle and call this Z.
RZ = SZ
RZ = SZ (common to both)
therefore: [tex]\Delta[/tex]RZQ =~ [tex]\Delta[/tex]SZQ
therefore: [tex]\Delta[/tex]QRZ = [tex]\Delta[/tex]QSZ
which results in: [tex]\angle[/tex]QRS = [tex]\angle[/tex]QSR
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