The triangles shown are congruent. Which of the following statements must be true?
(1 point)
A. YZ = JG
B.XY = JH
C.m angle Y=m angle J
D.m angle Y=m angle H
C. m angle Y = m angle J
To determine which of the statements must be true, we need to use the properties of congruent triangles.
When two triangles are congruent, their corresponding sides and corresponding angles will be equal.
Looking at the given options:
A. YZ = JG - We don't have any information about the lengths of YZ or JG, so we can't conclude whether they are equal or not.
B. XY = JH - Since the triangles are congruent, their corresponding sides will be equal. Therefore, XY = JH. This statement must be true.
C. m angle Y = m angle J - Corresponding angles of congruent triangles are equal. Therefore, m angle Y = m angle J. This statement must be true.
D. m angle Y = m angle H - We don't have any information about the angles Y or H, so we can't conclude whether they are equal or not.
So, the correct statements are B. XY = JH and C. m angle Y = m angle J.
To determine which of the following statements must be true, we need to analyze the given information. The triangles are said to be congruent, which means that they are exactly the same in size and shape.
When two triangles are congruent, their corresponding sides and angles are equal. So, let's examine the given triangles.
You mentioned triangles "XYZ" and "JHG" are congruent. To make it easier to refer to the triangles, let's label the vertices as follows:
- Triangle XYZ: X, Y, Z
- Triangle JHG: J, H, G
Now, let's analyze each option:
A. YZ = JG: This option suggests that the length of side YZ is equal to the length of side JG. Although the sides of congruent triangles are equal, we don't have enough information to determine if YZ is equal to JG. Therefore, we cannot conclude that option A is true.
B. XY = JH: This option suggests that the length of side XY is equal to the length of side JH. Similarly, we don't have enough information to determine if XY is equal to JH. Therefore, we cannot conclude that option B is true.
C. m angle Y = m angle J: This option states that the measure of angle Y is equal to the measure of angle J. Since the triangles are congruent, their corresponding angles are equal. Hence, option C, m angle Y = m angle J, must be true.
D. m angle Y = m angle H: This option claims that the measure of angle Y is equal to the measure of angle H. Based on the given information, we cannot determine if angle Y equals angle H. Therefore, we cannot conclude that option D is true.
In conclusion, the only statement that must be true is option C: m angle Y = m angle J.