Question

quadrilateral abcd is reflected across line m to create quadrilateral abcd. what is the perimeter of quadrilateral abcd? \boxed{} units

Explanation:

Step1: Recall reflection property

Reflection preserves side lengths, so corresponding sides of \(ABCD\) and \(A'B'C'D'\) are equal.

Step2: Identify corresponding sides

• \(BC = B'C' = 32\) (wait, no, \(BC\) in \(ABCD\): \(BC = 20\)? Wait, no, let's check again. Wait, \(ABCD\) has \(BC = 20\), \(CD = 30\), and from reflection, \(AB = A'B' = 22\), \(AD = A'D' = 32\). Wait, let's list all sides of \(ABCD\):
• \(BC = 20\) (given in \(ABCD\))
• \(CD = 30\) (given in \(ABCD\))
• \(AB = A'B' = 22\) (reflection, so \(AB = A'B'\))
• \(AD = A'D' = 32\) (reflection, so \(AD = A'D'\))

Step3: Calculate perimeter

Perimeter of \(ABCD\) is \(AB + BC + CD + AD = 22 + 20 + 30 + 32\).
First, \(22 + 20 = 42\), then \(30 + 32 = 62\), then \(42 + 62 = 104\).

Answer:

104