Lauren made the plan shown for proving that quadrilateral abcd with ab ≅ cd and bc ≅ da is a parallelogram, by showing that the opposite angles are congruent. plan: draw in diagonals ac and bd. the given information and the shared side ac along with the reflexive property can be used to prove by the sss congruence postulate. using cpctc, the same can be done for using the given information and the shared side bd¯¯¯¯¯¯¯¯. this will lead to therefore, abcd is a parallelogram because opposite angles are congruent.
It is given that the quadrilateral ABCD has AB ≅ CD and BC ≅ DA is a parallelogram, then in order to prove opposite angles of the parallelogram are equal, we take ΔABC and ΔADC,
Thus, by SSS rule, ΔABC ≅ ΔADC
By CPCT, ∠B=∠C
Also, from ΔABD and ΔBCD, we have
Thus, by SSS rule, ΔABD ≅ ΔBCD
By CPCT, ∠A=∠C
Since, opposite angles are equal,therefore ABCD is a parallelogram.
Draw in diagonals AC and BD. The given information and the shared side AC along with the Reflexive Property can be used to prove ΔABC ≅ ΔADC by the SSS Congruence Postulate. Using CPCTC, ∠B=∠C.The same can be done for ΔABD ≅ ΔBCD using the given information and the shared side BD. This will lead to ∠A=∠C. Therefore, ABCD is a parallelogram because opposite angles are congruent.
5. angle D’
6. Reflected over the y axis
m∠5 would be 31
Step-by-step explanation: This is because they are congruent.
Option f Angle Angle Side (AAS)
Given is a quadrilateral ABCD with two parallel sides AB and CD
AC the diagonal will also be a transveral and hence makes equal angles
(interior angles theorem)
Angle BAC = CAD
Also given that Angle ABC = angle CDA
AC =AC (reflexive property)
Hence by angle angle side axiom, the two triangles would be congruent
Option f( Angle Angle Side (AAS)
This problem can be answered through the Alternate interior angle theorem. The theorem states that if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are matching or congruent. So therefore, m ∠5 = m∠2, the answer is 31.
Then, because AC is shared by both triangles, we know it's the same for both, we now have two pairs congruent side and 1 congruent set of angles.
So side angle side.