Question

1. which statements can be made to prove that the 2 triangles are congruent? select all that apply. options: lk ≅ on, ∠l ≅ ∠o, ∠n ≅ ∠k, jl ≅ nm. (diagram shows two right triangles with angle labels 60°, 30°, and side congruence marks.)

Explanation:

1. Analyze \( \text{LK} \cong \text{ON} \):

• \( \angle K \) and \( \angle N \) are right angles (\( 90^\circ \)), so \( \angle K \cong \angle N \).
• The sides with one tick mark (e.g., \( JK \) and \( NM \)) are congruent, and sides with two ticks (e.g., \( LK \) and \( ON \)) are congruent.
• By SAS (Side - Angle - Side) congruence, if \( \text{LK} \cong \text{ON} \), along with the right angle and the single - ticked side, this helps prove congruence.

1. Analyze \( \angle L \cong \angle O \):

• Both \( \angle L \) and \( \angle O \) are \( 30^\circ \) (given in the triangles).
• The right angles (\( \angle K \cong \angle N \)) and the angles \( \angle L \cong \angle O \), along with the side - angle - side or angle - angle - side relationships (since we have right angles and \( 30^\circ \) angles, the third angle will be \( 60^\circ \), and we have congruent sides from the tick marks) support triangle congruence.

1. Analyze \( \angle N \cong \angle K \):

• Both \( \angle N \) and \( \angle K \) are right angles (\( 90^\circ \)), so they are congruent. This is a key angle for congruence criteria (e.g., SAS, ASA) as we have other congruent sides and angles.

1. Analyze \( \text{JL} \cong \text{OM} \):

• The sides with three tick marks ( \( JL \) and \( OM \)) are congruent. Along with the right angles and the other congruent sides (from tick marks), this satisfies congruence criteria (e.g., SSS or SAS) to prove the triangles are congruent.

Answer:

• \( \text{LK} \cong \text{ON} \) (checked)
• \( \angle L \cong \angle O \) (checked)
• \( \angle N \cong \angle K \) (checked)
• \( \text{JL} \cong \text{OM} \) (checked)