Question
Based on the given information, what can you conclude, and why? Two triangles are formed by intersecting segments. Segment I L intersects segment H K at point J. I and H are connected by a segment. K and L are connected by a segment.
Given: angleH congruent to angleL, modifying above H J with barcongruent to modifying above J L with bar
(1 point)
Responses
triangleHIJ congruent to triangleLKJ by ASA
Image with alt text: triangle HIJ Image with alt text: congruent to Image with alt text: triangle LKJ by ASA
triangleHIJ congruent totriangleJLK by SAS
Image with alt text: triangle HIJ Image with alt text: congruent to Image with alt text: triangle JLK by SAS
triangleHIJ congruent totriangleJLK by ASA
Image with alt text: triangle HIJ Image with alt text: congruent to Image with alt text: triangle JLK by ASA
triangleHIJ congruent totriangleLKJ by SAS
Based on the given information, we can conclude that triangle HIJ is congruent to triangle LKJ by ASA (Angle-Side-Angle) congruence. This is because angle H is congruent to angle L, and the segments HJ and LJ are congruent.
Correct response:
triangleHIJ congruent to triangleLKJ by SAS
To determine the correct conclusion based on the given information, we can use triangle congruence criteria. In this case, we have two triangles formed:
- Triangle HIJ
- Triangle LKJ
We are given the following information:
1. angle H is congruent to angle L (angleH ≅ angleL)
2. segment HJ is congruent to segment JL (HJ ≅ JL)
To determine the congruence between the triangles, we need to use a triangle congruence criterion. The two angles and the included side are congruent, so we can use the ASA (Angle-Side-Angle) or the SAS (Side-Angle-Side) congruence criterion.
From the given information, we can see that angle H (vertex angle of triangle HIJ) is congruent to angle L (vertex angle of triangle LKJ). Additionally, segment HJ (side of triangle HIJ) is congruent to segment JL (side of triangle LKJ).
Therefore, we can conclude that triangle HIJ is congruent to triangle LKJ by the SAS (Side-Angle-Side) congruence criterion.
The correct response is:
triangleHIJ congruent to triangleLKJ by SAS