Question

Fill in the missing statement and reason of the proof below.

Given: start overline, A, B, end overline, \cong, start overline, C, D, end overline
AB
≅
CD
and start overline, B, C, end overline, \cong, start overline, A, D, end overline, .
BC
≅
AD
.

Prove: angle, B, A, D, \cong, angle, B, C, D∠BAD≅∠BCD.
Step Statement Reason
1
start overline, A, B, end overline, \cong, start overline, C, D, end overline
AB
≅
CD

start overline, B, C, end overline, \cong, start overline, A, D, end overline
BC
≅
AD

Given
2
start overline, A, C, end overline, \cong, start overline, A, C, end overline
AC
≅
AC

Reflexive Property
3
triangle, A, B, C, \cong, triangle, C, D, A△ABC≅△CDA
SSS
4
5
angle, B, C, A, \cong, angle, C, A, D∠BCA≅∠CAD
Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
6
angle, B, A, D, \cong, angle, B, C, D∠BAD≅∠BCD
Congruent angles added to congruent angles form congruent angles
A
B
C
D

Answer 1

We can see here that the missing statement and reason of the proof is:

∠BCA ≅ ∠CAD - Alternating angles.

Alternating angles are a pair of non-adjacent angles that lie on opposite sides of a transversal line and are formed when a straight line intersects two other lines. These angles are also known as "corresponding angles" or "Z-angles."

When a transversal crosses two parallel lines, it creates a series of angles. Alternating angles are pairs of angles that are congruent or equal to each other. In other words, they have the same measure or size.