65.0k views
5 votes
Solving a proof I know how to start it just confused how to put it all together

Solving a proof I know how to start it just confused how to put it all together-example-1

1 Answer

3 votes

Given that ABCD is a parallelogram, prove that


\begin{gathered} \bar{AB}\cong\bar{CD} \\ \bar{BC}=\bar{DA} \end{gathered}

step 1: Sketch the parallelogram

step 2: The diagonal AC, divides the parallelogram into two triangles


\begin{gathered} \Delta ADC\text{ and }\Delta ABC \\ Note\text{ that,} \\ \angle DAC=\angle ACB\text{ ( the angles are alternate)} \\ \angle DCA=\angle BAC\text{ (the angles are alternate)} \\ side\text{ AC = AC (common sides for both triangles)} \end{gathered}

step 3: By the ASA (Angle-Side-Angle) congruency theorem,


\begin{gathered} \Delta ADC\cong\Delta ABC \\ (The\text{ two triangles are congruent)} \end{gathered}

Hence, by CPCT (corresponding parts of congruent triangles)


\begin{gathered} \bar{AB}\cong\bar{CD}\text{ } \\ \bar{BC}\cong\bar{DA} \end{gathered}

Solving a proof I know how to start it just confused how to put it all together-example-1
User Mohan Gulati
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories