Question

Your sister says that the angles ∠DCA and ∠BCA are supplementary angles. Is she correct? Explain your reasoning.

Is triangle DCA congruent to triangle BCA? Explain.

Answer 1

Proving congruency:

CA = CA, reflexive

m ∠DCA = m ∠BAC, alt interior ∠

m ∠BCA = m ∠DAC, alt interior ∠

triangle DCA = triangle BCA, ASA

Supplementary angles means a pair of angles adding to 180 degrees.

180 degrees would be a straight angle.

∠DCA + ∠BCA = ∠DCB, not a straight angle.

Hope this helped.