Question

question 5 of 5
drag the tiles to the boxes to form correct pairs.
given: $overline{ab}paralleloverline{cd}$ and $overline{ad}paralleloverline{cb}$
prove: $overline{ab}congoverline{cd}$ and $overline{ad}congoverline{cb}$
match each step of the proof to its justification.
asa
two points define a line
reflexive property of congruence
cpctc
given
alternate interior angles theorem

Explanation:

Step1: Draw diagonal AC

Two - points define a line.

Step2: $\angle BAC\cong\angle DCA$ and $\angle ACB\cong\angle CAD$

Alternate interior angles theorem (since $\overline{AB}\parallel\overline{CD}$ and $\overline{AD}\parallel\overline{CB}$).

Step3: $AC = AC$

Reflexive property of congruence.

Step4: $\triangle ABC\cong\triangle CDA$

ASA (by the angles and side shown above).

Step5: $\overline{AB}\cong\overline{CD}$ and $\overline{AD}\cong\overline{CB}$

CPCTC (Corresponding Parts of Congruent Triangles are Congruent).

Answer:

1. Drawing diagonal AC - two points define a line
2. $\angle BAC\cong\angle DCA$ and $\angle ACB\cong\angle CAD$ - alternate interior angles theorem
3. $AC = AC$ - reflexive property of congruence
4. $\triangle ABC\cong\triangle CDA$ - ASA
5. $\overline{AB}\cong\overline{CD}$ and $\overline{AD}\cong\overline{CB}$ - CPCTC