Answer:
1. ΔUJN ≅ ΔUGN by SAS rule of congruency
2. Side Angle Side Rule of congruency
3. JN ≅ GN, ∠JUN ≅ ∠NUG, ∠UNJ ≅ ∠UNG, NU ≅ NU
4. UN bisects angle ∠JUG and UN bisects segment JG
Step-by-step explanation:
The given figure consists of three triangles
1. ΔUJN, 2. ΔUGN, and 3. ΔUJG
Whereby segment UN is perpendicular to segment JG, we have;
ΔUJN and ΔUGN are right triangles
∴ ∠UNJ = ∠UNG = 90° by definition of segment UN being perpendicular to segment JG
NU ≅ NU by reflexive property
Whereby UN bisects ∠JUG and segment JG, we have;
JN = GN by definition of a bisected segment
Therefore, we have;
1. ΔUJN ≅ ΔUGN by SAS rule of congruency
2. Side Angle Side Rule of congruency
3. JN ≅ GN, ∠JUN ≅ ∠NUG, ∠UNJ ≅ ∠UNG, NU ≅ NU
4. UN bisects angle ∠JUG and UN bisects segment JG
