Question

ometry sem a geometry congruence: sss and hl examine this figure. which two pieces of information, if true, would help to prove that ( \triangle lmp cong \triangle nmp ) by hl? choose two correct answers. ( overline { ml } cong overline { mn } ) line mk is the perpendicular bisector of ( overline { ln } ). ( overline { ml } cong overline { mp } ) point p is the midpoint of ( overline { mk } ). ( overline { pk } cong overline { pk } )

Explanation:

• For the Hypotenuse - Leg (HL) congruence criterion in right - triangles:
• Condition 1: Right - angles
• If line \(MK\) is the perpendicular bisector of \(\overline{LN}\), then \(\angle LPM=\angle NPM = 90^{\circ}\) (by the definition of a perpendicular bisector). So, \(\triangle LMP\) and \(\triangle NMP\) are right - triangles.
• Condition 2: Hypotenuse equality
• If \(\overline{ML}\cong\overline{MN}\), then the hypotenuses of the right - triangles \(\triangle LMP\) and \(\triangle NMP\) are congruent. Also, \(\overline{MP}\) is the common leg for both right - triangles \(\triangle LMP\) and \(\triangle NMP\).

Answer:

\(\overline{ML}\cong\overline{MN}\), Line \(MK\) is the perpendicular bisector of \(\overline{LN}\)