Question

The proof that TriangleMNG ≅ TriangleKJG is shown.

Given: AngleN and AngleJ are right angles; NG ≅ JG
Prove: TriangleMNG ≅ TriangleKJG

Triangles M N G and J K G share point G. Angles M N G and G J K are right angles. Sides N G and G J are congruent.
What is the missing reason in the proof?

A 2-column table has 5 rows. Column 1 is labeled Statement with entries line segment N G is-congruent-to line segment J G, angle N and angle J are right angles, angle M G N is-congruent-to angle K G J, angle N is-congruent-to angle J, triangle M N G is-congruent-to triangle K J G. Column 2 is labeled reason with entries given, given, vertical angles are congruent, right angles are congruent, and question mark.
the reflexive property
ASA
AAS
the third angle theorem

Answer 1

ASA

You have ∠N ≅ ∠J (right angles), ∠MGN ≅ ∠KGJ (vertical angles), and NG ≅ JG (included side between those two angles), so by Angle–Side–Angle the two triangles are congruent.