Given: AB is congruent to CD and BC is congruent to AD Prove: AB ll CD and BC ll AD

Mathematics

1 answer:

kifflom [539]2 years ago

4 0

<h2>Given</h2>

A quadrilateral ABCD with opposite pairs of sides being congruent.

<h2>To prove</h2>

Opposite sides are parallel.

<h2>Solution</h2>

We'll prove first the triangles formed by diagonal are congruent then we'll prove the angles on either side of diagonal are congruent.

<u>The steps are:</u>

Step ⇒ Statement ⇒ Reason

=============================================================

1 ⇒ AB ≅ CD and BC ≅ AD ⇒ Given
2 ⇒ AC = CA ⇒ Common side
3 ⇒ ΔABC ≅ ΔCDA ⇒ Side-side-side congruence
4 ⇒ ∠BAC ≅ ∠DCA ⇒ Corresponding angles of congruent triangles
5 ⇒ ∠BAC and ∠DCA are alternate interior angles ⇒ Definition of alternate interior angles
6 ⇒ AB║CD ⇒ The converse of alternate interior angles theorem
7 ⇒ ∠BCA ≅ ∠DAC ⇒ Corresponding angles of congruent triangles
8 ⇒ ∠BCA & ∠DAC are alternate interior angles ⇒ Definition of alternate interior angles
9 ⇒ BC║AD ⇒ The converse of alternate interior angles theorem