Question

Explain how to prove that the statement "JM is congruent to LM" is true. In triangle JKL, side JK and side KL are marked with a single tick mark. A point M is marked on side JL such that line segment KM is perpendicular to side JL. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button, or touchpad. Responses can also be moved by dragging with a mouse. Triangle JMK is congruent to Triangle LMK by the congruence theorem. Because corresponding parts of the congruent triangles are congruent, JM is congruent to LM.

Answer 1

To prove that JM is congruent to LM, we use the HL Congruence Theorem based on the given information that JK is congruent to KL and KM is perpendicular to JL, thereby showing that triangle JMK is congruent to triangle LMK, which implies congruency of JM and LM.

Step-by-step explanation:

To prove that the statement "JM is congruent to LM" is true, we look at the given information in triangle JKL. Side JK and side KL are marked with single tick marks indicating they are congruent (JK ≅ KL). Since point M lies on side JL such that segment KM is perpendicular to JL, we can consider triangles JMK and LMK. Because we have a right angle at M (KM is perpendicular to JL), side KM is common to both triangles, and sides JK and KL are congruent, we can conclude that these two triangles are congruent by the HL (Hypotenuse-Leg) Congruence Theorem. As a result, corresponding parts of congruent triangles are congruent (CPCTC), which implies that segment JM is congruent to segment LM.