Answer:
A, C, D
Step-by-step explanation:
Consider triangles NKL and NML. These triangles are right triangles, because
[tex]m\angle K=m\angle M=90^{\circ}[/tex]
In these right triangles:
- [tex]\overline{NL}\cong \overline {NL}[/tex] - reflexive property;
- [tex]\angle KLN\cong \angle MLN[/tex] - given
Thus, triangles NKL and NML by HA postulate. Congruent triangles have congruent corresponding parts, so
[tex]\overline{KN}\cong \overline{NM}\\ \\\overline{KL}\cong \overline{LM}\ [\text{option D is true}][/tex]
Since
[tex]\overline{KN}\cong \overline{NM},[/tex]
then
[tex]7x-4=5x+12\\ \\7x-5x=12+4\\ \\2x=16\\ \\x=8\ [\text{option A is true}]\\ \\MN=KN=7\cdot 8-4=56-4=52\ [\text{option C is true}][/tex]
Option B is false, because KN=52 units.
Option E is false, because LN is congruent KN, not LM
