Question

Which of the following statements is true if m∠E = m∠Y and m∠F = m∠X?

triangles EFG and YXZ in which triangle YXZ is larger than EFG

segment EF ~ segment XZ.
The measure of segment YZ is three times the size of segment EG.
segment FE over segment XY equals segment EG over segment YZ equals segment GF over segment ZX
There is a sequence of rigid motions that map ΔEFG onto ΔYXZ.

Answer 1

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

$\frac{FE}{XY}=\frac{EG}{YZ}=\frac{GF}{ZX}$

therefore

segment FE over segment XY equals segment EG over segment YZ equals segment GF over segment ZX

Answer 2

The true statement is:

segment FE over segment XY equals segment EG over segment YZ equals segment GF over segment ZX

Further explanation

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 )

$\texttt{ }$

Because of the similarity , then:

FE : XY = EG : YZ = GF : ZX

$\texttt{ }$

Conclusion:

ΔEFG is similar to ΔYXZ.

Segment FE over segment XY equals segment EG over segment YZ equals segment GF over segment ZX , i.e:

$\large {\boxed{ \frac{FE}{XY} = \frac{EG}{YZ} = \frac{GF}{ZX} } }$

$\texttt{ }$

Learn more

• Calculate Angle in Triangle : https://brainly.com/question/12438587
• Periodic Functions and Trigonometry : https://brainly.com/question/9718382
• Trigonometry Formula : https://brainly.com/question/12668178

Answer details

Grade: College

Subject: Mathematics

Chapter: Trigonometry

Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse , Triangle , Fraction , Lowest , Function , Angle