Question

drag a statement to each empty box to complete karas proof that \\( \angle d a b \\) is congruent to \\( \angle b c d \\).

\\( \

$$\begin{array} { | l | l | } \\hline \\text { statement } & \\text { karas proof } \\\\ \\hline \\text { draw diagonal } b d \\text {; through any two points there exists exactly one line. } & 1 \\overline { a b } \\cong \\overline { d c } \\text { and } \\overline { b c } \\cong \\overline { a d } \\text {. } \\text { given } \\\\ \\hline & 2 \\\\ \\hline \\angle d a b \\cong \\angle b c d \\text {; corresponding parts of congruent triangles are } & 3 \\\\ \\text { congruent. } & \\\\ \\hline \\overline { d b } \\cong \\overline { b d } \\text {; reflexive property } & 4 \\\\ \\hline & 5 \\\\ \\hline \\end{array}$$

\\)

Explanation:

Step1: Arrange the statements in order

The reflexive property \(DB\cong BD\) (statement 4) should come before using the Side - Side - Side Congruence. So statement 4 is step 2.

Step2: Apply SSS congruence

After having \(AB\cong DC\), \(BC\cong AD\), and \(DB\cong BD\), by the Side - Side - Side Congruence (\(\triangle ABD\cong\triangle CDB\), statement 2), this is step 3.

Step3: Use CPCTC

Since \(\triangle ABD\cong\triangle CDB\), then by the Corresponding Parts of Congruent Triangles are Congruent (\(\angle DAB\cong\angle BCD\), statement 3), this is step 4.

Step4: Final order

The order of the statements:

1. \(AB\cong DC\) and \(BC\cong AD\) (given)
2. \(DB\cong BD\) (reflexive property)
3. \(\triangle ABD\cong\triangle CDB\) (Side - Side - Side Congruence)
4. \(\angle DAB\cong\angle BCD\) (corresponding parts of congruent triangles are congruent)

Answer:

1. \(DB\cong BD\); reflexive property
2. \(\triangle ABD\cong\triangle CDB\); Side - Side - Side Congruence
3. \(\angle DAB\cong\angle BCD\); corresponding parts of congruent triangles are congruent