<h2>
Answer:</h2>
The student who labeled the triangle correct such that:
ΔABC ~ ΔXYZ
is: Kai
<h2>
Step-by-step explanation:</h2>
For ΔABC ~ ΔXYZ
we must have that:
m∠A=m∠X
m∠B=m∠Y
and m∠C=m∠Z
From the labeling that is done by <u>Tatyanna</u> we see that :
m∠C≠m∠Z
Hence, Tatyana labeled the triangles incorrect.
Similarly the labeling done by <u>Simon</u> is also incorrect.
Since according to him m∠A≠m∠X
( Since, by looking at the triangle XYZ we are given two angle measure with the help of which the third angle measure could be calculated by using the property that the sum of all the angles of a triangle is: 180°
i.e. ∠X+∠Y+∠Z=180
i.e. ∠X+63.2+58.4=180
i.e. ∠X=180°-(63.2°+58.4°)
i.e. ∠X=180°-(121.6°)
i.e. ∠X=58.4° )
Hence, Simon labeled the triangle incorrect.
<u>Anders--</u>
( In ΔABC we have:
∠A+∠B+∠C=180°
⇒ 59.8°+60.6°+∠C=180°
⇒ ∠C=59.6° )
Here as m∠C≠m∠Z
Hence, Anders labeled the triangle incorrect.
<u>Kai--</u>
( In ΔABC we have:
∠A+∠B+∠C=180°
⇒ ∠A+60.9°+57.7°=180°
⇒ ∠A=61.4°
Similarly in ΔXYZ we get:
∠Y=60.9° )
Hence, Kai labeled the triangle correct.
Since, m∠A=m∠X
m∠B=m∠Y
m∠C=m∠Z
