Question

Based on the given diagram, complete the flowchart proof below. Note that the last statement and reason have both been filled in for you.(this part got cut off in the first photo)

Answer 1

reflexive property

Parallel lines cut by a transversal form congruent alternate angles

Parallel lines cut by a transversal form congruent alternate angles

Explanation:

We use the diagram to determine the statements:

from the diagram ABCD:

∠BAC and ∠DCA are alternate angles and are equal

∠BAC = ∠DCA (angle)

Reason: Parallel lines cut by a transversal form congruent alternate angles

side AC is common to triangle ABC and triangle ADC

AC = AC (side)

when a side equals itself, ti is called a reflexive property

Reason: reflexive property

∠BCA and ∠DAC are alternate angles and are equal

∠BCA = ∠DAC (angle)

Reason: Parallel lines cut by a transversal form congruent alternate angles

Hence, the two triangles are congruent as the corresponding sides and angle of each are equal

ΔABC ≅ ΔCDA

Reason: ASA (angle-side-angle)