Answer:
segment FE over segment XY equals segment EG over segment YZ equals segment GF over segment ZX
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
If m∠E = m∠Y and m∠F = m∠X
then
Triangles EFG and YXZ are similar by AA Similarity Theorem
Remember that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem
The corresponding sides are
FE and XY
EG and YZ
GF and ZX
so therefore
segment FE over segment XY equals segment EG over segment YZ equals segment GF over segment ZX Firstly , let us learn about trigonometry in mathematics.
Suppose the ΔABC is a right triangle and ∠A is 90°.
sin ∠A = opposite / hypotenuse
cos ∠A = adjacent / hypotenuse
tan ∠A = opposite / adjacent
Let us now tackle the problem!
A similar triangle has the same angle, in other words the triangle has the same shape but different sizes.
From the figure in the attachment , we can conclude that:
m∠E = m∠Y
m∠F= m∠X
m∠G = m∠Z
∴ ΔEFG ~ ΔYXZ ( ΔEFG is similar to ΔYXZ )
Because of the similarity , then:
FE : XY = EG : YZ = GF : ZX
Conclusion:
ΔFG is similar to ΔYXZ.
Segment FE over segment XY equals segment EG over segment YZ equals segment GF over segment ZX , i.e:
Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse , Triangle , Fraction , Lowest , Function , Angle
