Question

I need some help with this

Answer 1

A, C, D

Explanation:

Consider triangles NKL and NML. These triangles are right triangles, because

`m\angle K=m\angle M=90^(\circ)`

In these right triangles:

• 
  `\overline{NL}\cong \overline {NL}` - reflexive property;
• 
  `\angle KLN\cong \angle MLN` - given

Thus, triangles NKL and NML by HA postulate. Congruent triangles have congruent corresponding parts, so

`\overline{KN}\cong \overline{NM}\\ \\\overline{KL}\cong \overline{LM}\ [\text{option D is true}]`

Since

`\overline{KN}\cong \overline{NM},`

then

`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}]`

Option B is false, because KN=52 units.

Option E is false, because LN is congruent KN, not LM