Question

triangle congruence: asa and aas
two rigid transformations are used to map △jkl to △mnq. the first is a translation of vertex l to vertex q. what is the second transformation?
options:

• a reflection across the line containing (overline{lk})
• a reflection across the line containing (overline{jk})
• a rotation about point k
• a rotation about point l

Explanation:

Step1: Analyze the first transformation

The first transformation is a translation of vertex \( L \) to vertex \( Q \). Now we need to find the second transformation that maps \( \triangle JKL \) to \( \triangle MNQ \).

Step2: Analyze the options

• Let's consider the triangles. After translating \( L \) to \( Q \), we need to check the rotation. Rotation about point \( L \) (now \( Q \) after translation? Wait, no, the first transformation is translation of \( L \) to \( Q \). Then, to map the triangle, a rotation about point \( L \) (original \( L \), now translated to \( Q \))? Wait, looking at the triangles, the angles and sides: \( \angle J \) and \( \angle M \) are equal, \( \angle L \) and \( \angle Q \) are equal, and sides \( JL \) and \( MQ \) are equal (marked with ticks). After translating \( L \) to \( Q \), a rotation about point \( L \) (now \( Q \))? Wait, the correct second transformation is a rotation about point \( L \) (original \( L \), which is now at \( Q \) after translation? Wait, no, let's re - examine. The triangles \( \triangle JKL \) and \( \triangle MNQ \): after translating \( L \) to \( Q \), the next transformation to align the other vertices would be a rotation about point \( L \) (since \( L \) is now at \( Q \), rotating about \( L \) (now \( Q \)) to map \( K \) to \( N \) and \( J \) to \( M \)). Wait, among the options, "a rotation about point \( L \)" is the correct one. Wait, let's check the options again. The options are:
• a reflection across the line containing \( \overline{LK} \)
• a reflection across the line containing \( \overline{JK} \)
• a rotation about point \( K \)
• a rotation about point \( L \)

After translating \( L \) to \( Q \), to map \( \triangle JKL \) to \( \triangle MNQ \), we need to rotate about point \( L \) (now \( Q \)) to align the sides and angles. So the second transformation is a rotation about point \( L \).

Answer:

a rotation about point \( L \)