Question

in quadrilateral BADC, AB= AD and BC= DC. The line AC is a line of symmetry for this quadrilateral. Based on the line of symmetry, explain why the angles ACB and ACD have the same measure​

Answer 1

Answer:

See explanation

Step-by-step explanation:

In quadrilateral BADC,

AB= AD

BC= DC

AC is a line of symmetry for this quadrilateral

Consider triangles BAC and DAC. In these triangles,

• AB = AD - given
• BC = DC - given
• AC = AC - reflexive property

So, ΔBAC ≅ ΔDAC by SSS postulate.

Congruent triangles have congruent corresponding sides and angles, so

m∠ACB = m∠ACD

Another way: The line of symmetry can be defined as the line that divides the figure into two identical figures. Thus, ΔBAC and ΔDAC are identical (congruent) and have congruent corresponding sides and angles.