Question

Given Δ XYZ ≅ Δ EGF, find the measurements of the unknown sides and angles.

Answer 1

The two triangles are similar and equal therefore; It means the corresponding sides are equal and the corresponding angles are equal. Hence;
 ZX=EF, thus,ZX = 1.3 in. 
EG = XY, thus, EG = 3.0 in.
m∠ X = m∠E, thus m ∠X = 48°
m∠ G = m∠Y, and angles in a triangle add up to 180 thus;
  m ∠ G=180- (107 +48) = 25°

Answer 2

The triangles are given to be congruent which means that their corresponding angles and sides will have to have similar measures and similar lengths. 

a. ZX = __ in
 The length of ZX is equal to the length of FE. Hence, the length should be equal to 1.3 in. 

b. EG = __ in
 The length of EG is equal to the length of XY. From the figure, the answer should be 3.0 in.

c. m∠X = __°
 The measure of angle x should be equal to the measure of angle E. This is given to be equal to 48°.

d. m∠G
  The measure of angle F is equal to the measure of angle Z. Th measure of angle F should then be equal to 107°. In the triangle in the right, the measure of angle E is 48°, the measure of angle F is 107°, subtracting the sum of these angles from 180°, we are then left with measure of angle G which is equal to 25°.