Question

(some zs are something else but come up as z expect last one!) In A ABC, m ZA=62° and m ZB=39° In AXYZ, m ZY=39° and m ZZ = 790 Julie says that the triangles are congruent because all the corresponding angles have the same measure. Ramiro says that there is not enough information given to determine whether the triangles are similar, congruent, or neither. 1. Which student correct? (1 point) Explain your reasoning and include all relevant calculations. (2 points)

Answer 1

1) Julie is correct.

2) All of the explanation and calculation is provided below.

Ramiro is wrong because the information provided is sufficient to obtain all the other requiired information and determine if the two triangles are similar or not.

Step-by-step explanation

To answer this question, we need to first note that the sum of angles in a triangle is 180°.

So, we need to first find the third angle for each of the two triangles described before answering the question.

In triangle ABC

Angle A = 62°

Angle B = 39°

Angle A + Angle B + Angle C = 180°

62° + 39° + Angle C = 180°

101° + Angle C = 180°

Angle C = 180° - 101°

Angle C = 79°

In triangle XYZ

Angle Y = 39°

Angle Z = 79°

So,

Angle X + Angle Y + Angle Z = 180°

Angle X + 39° + 79° = 180°

Angle X + 118° = 180°

Angle X = 180° - 118°

Angle X = 62°

So, we can see that the three angles for the two triangles are the same.

And one of the conditions for two triangles to be congruent is for all of their corresponding angles to be the same measures.

1) Hence, Julie is correct.

2) All of the explanation and calculation is provided above.

Ramiro is wrong because the information provided is sufficient to obtain all the other requiired information and determine if the two triangles are similar or not.

Hope this Helps!!!