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

Okay so, ABC and ADC have the same measurements as they are a replica of each other. The line of symmetry line is AC meaning that ABC and ADC are the same shapes. Meaning they would be the exact same measurements as it is just a reflection.

Explanation:

Hope this helps. I am a flvs student so I knew the question without the image. But yeah hope this helps. <3

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Answer 2

See explanation

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.