Which of the following statements is true about the triangles below?
The figure shows triangle J K N and triangle L K M formed by intersecting segments J M and N L at point K. Segment J K is marked with 2 hash marks. Segment K L is marked with 2 hash marks. Segment N K is marked with 1 hash mark. Segment K M is marked with 1 hash mark.
(1 point)
Responses
Triangle Upper J Upper K Upper N congruent to triangle Upper M Upper K Upper Lby SSS
Image with alt text: Triangle Upper J Upper K Upper N congruent to triangle Upper M Upper K Upper L by SSS
Triangle Upper J Upper K Upper N congruent to triangle Upper N Upper K Upper Jby AAS
Image with alt text: Triangle Upper J Upper K Upper N congruent to triangle Upper N Upper K Upper J by AAS
Triangle Upper J Upper K Upper N congruent to triangle Upper K Upper L Upper Mby ASA
Image with alt text: Triangle Upper J Upper K Upper N congruent to triangle Upper K Upper L Upper M by ASA
Triangle Upper J Upper K Upper N congruent to triangle Upper L Upper K Upper Mby SAS
Triangle JKN is congruent to triangle LKM by ASA.
The correct statement is: Triangle JKN is congruent to triangle LKM by SAS (Side-Angle-Side).
To determine which of the given statements is true about the triangles, we need to analyze the markings on the segments and consider the congruence criteria.
The given markings indicate the lengths of the segments. Let's look at each statement and the corresponding congruence criteria:
1. Triangle JKN congruent to triangle MKL by SSS (Side-Side-Side): This criteria states that if the three sides of one triangle are congruent to the corresponding three sides of another triangle, then the triangles are congruent. However, we don't have enough information about the side lengths to determine if this statement is true.
2. Triangle JKN congruent to triangle NKJ by AAS (Angle-Angle-Side): This criteria states that if two angles and a non-included side of one triangle are congruent to the corresponding two angles and non-included side of another triangle, then the triangles are congruent. However, we don't have any information about the angles in the triangles, so we cannot determine if this statement is true.
3. Triangle JKN congruent to triangle KLM by ASA (Angle-Side-Angle): This criteria states that if two angles and the included side of one triangle are congruent to the corresponding two angles and included side of another triangle, then the triangles are congruent. From the markings, we can observe that segment JK is marked with 2 hash marks, segment KL is marked with 2 hash marks, and segment NK is marked with 1 hash mark. Therefore, we can say that the included angles between these segments (angle JKN and angle KLM) are congruent, and the included side (NK) between these angles is congruent as well. So, we can conclude that Triangle JKN is congruent to Triangle KLM by ASA.
4. Triangle JKN congruent to triangle LKM by SAS (Side-Angle-Side): This criteria states that if two sides and the included angle of one triangle are congruent to the corresponding two sides and included angle of another triangle, then the triangles are congruent. However, we don't have any information about the angles in the triangles, so we cannot determine if this statement is true.
Based on the given information, the statement that is true is: "Triangle JKN congruent to triangle KLM by ASA."