Question

5 finish the triangle proof by dragging the correct reasons to their box. there will be two extra unused reasons! given: ∠bad ≅ ∠dcb, bc || da prove: ab ≅ cd ab ≅ cd bd ≅ bd bc || da asa corresponding angles reflexive property △bad ≅ △dcb ∠adb ≅ ∠cbd ∠bad ≅ ∠dcb alternate interior angles given given aas

Explanation:

Step1: Write the first statement and reason

Statement 1: $\angle BAD\cong\angle DCB$. Reason 1: Given.

Step2: Write the second statement and reason

Statement 2: $BC\parallel DA$. Reason 2: Given.

Step3: Write the third statement and reason

Since $BC\parallel DA$, by the Alternate Interior Angles Theorem, $\angle ADB\cong\angle CBD$. Statement 3: $\angle ADB\cong\angle CBD$. Reason 3: Alternate Interior Angles.

Step4: Write the fourth statement and reason

Statement 4: $BD = BD$. Reason 4: Reflexive Property.

Step5: Write the fifth statement and reason

By the AAS (Angle - Angle - Side) congruence criterion for triangles, $\triangle BAD\cong\triangle DCB$. Statement 5: $\triangle BAD\cong\triangle DCB$. Reason 5: AAS.

Step6: Write the sixth statement and reason

Since $\triangle BAD\cong\triangle DCB$, by CPCTC (Corresponding Parts of Congruent Triangles are Congruent), $AB\cong CD$. Statement 6: $AB\cong CD$. Reason 6: CPCTC.

Answer:

Statement	Reason
2. $BC\parallel DA$	2. Given
3. $\angle ADB\cong\angle CBD$	3. Alternate Interior Angles
4. $BD = BD$	4. Reflexive Property
5. $\triangle BAD\cong\triangle DCB$	5. AAS
6. $AB\cong CD$	6. CPCTC