The triangles shown are congruent. Which of the following statements must be true?
The image shows two triangles. The first has points labeled X, Y and Z, and the second has points labeled J, H and G. One corresponding side and two corresponding angles on each triangle are congruent to the other.
(1 point)
Responses
Upper Y Upper Z equals Upper J Upper G
Image with alt text: Upper Y Upper Z equals Upper J Upper G
Upper X Upper Y equals Upper J Upper H
Image with alt text: Upper X Upper Y equals Upper J Upper H
m angle Upper Y equals m angle Upper J
Image with alt text: m angle Upper Y equals m angle Upper J
m angle Upper Y equals m angle Upper H
m angle Upper Y equals m angle Upper H
The statement that must be true is:
m angle Upper Y equals m angle Upper J
Since the two triangles are congruent, it means that their corresponding angles are also congruent. Therefore, angle Upper Y in the first triangle must be congruent to angle Upper J in the second triangle.
To determine which statement is true, we need to analyze the given information about the congruent triangles.
The triangles are congruent, which means that their corresponding sides and corresponding angles are equal. Let's break down each option and see which one aligns with this information.
Option 1: Upper Y Upper Z equals Upper J Upper G
This statement compares the lengths of two sides of the triangles. However, since we do not have any information about the lengths of the sides, we cannot determine if this statement is true or not. Therefore, Option 1 may or may not be true.
Option 2: Upper X Upper Y equals Upper J Upper H
This statement compares the lengths of two sides of the triangles. Similarly to Option 1, without any information about side lengths, we cannot determine if this statement is true or not. Therefore, Option 2 may or may not be true.
Option 3: m angle Upper Y equals m angle Upper J
This statement compares the measures of two angles of the triangles. It aligns with the given information that two corresponding angles are congruent. Therefore, Option 3 must be true.
Option 4: m angle Upper Y equals m angle Upper H
This statement also compares the measures of two angles of the triangles. However, there is no information given about the angles at points H and G. Therefore, we cannot determine if this statement is true or not. Therefore, Option 4 may or may not be true.
In conclusion, the statement that must be true is:
m angle Upper Y equals m angle Upper J.