Answer:
Show that the ratios StartFraction UV/XY, WU/ZX, and WV/ZY are equivalent.
Step-by-step explanation:
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Two triangles are similar but not congruent if they have three congruent angles but the side lengths are not equal
The two triangles can be shown to be similar given that the ratios of the corresponding sides ΔWUV and ΔYXZ are constant
Reason:
Known parameters are;
ΔWUV and ΔXZY are shown
∠VUW ≅ ∠YXZ
∠UWV ≅ ∠XZY
∠UVW ≅ ∠ZYX
Length of side [tex]\overline {VW}[/tex] = 60
Length of side [tex]\overline {VU}[/tex] = 50
Length of side [tex]\overline {UW}[/tex] = 40
Length of side [tex]\overline {ZY}[/tex] = 48
Length of side [tex]\overline {YX}[/tex] = 40
Length of side [tex]\overline {XZ}[/tex] = 32
The ratio of the sides are;
[tex]\dfrac{\overline {VW}}{\overline {ZY}} = \dfrac{60}{48} = \dfrac{5}{4}[/tex]
[tex]\dfrac{\overline {VU}}{\overline {YX}} = \dfrac{50}{40} = \dfrac{5}{4}[/tex]
[tex]\dfrac{\overline {UW}}{\overline {XZ}} = \dfrac{40}{32} = \dfrac{5}{4}[/tex]
Therefore, given that the angles of ΔWUV and ΔXZY are all congruent, and the sides of triangle ΔWUV and ΔXZY have a constant proportion, we have that the two triangles are congruent by Side-Side-Side SSS congruency theorem, and we have;
ΔWUV ~ ΔYXZ given that ΔYXZ is scaled drawing of ΔWUV
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