Question

quadrilateral efgh is a scaled copy of quadrilateral abcd. which of the following statements is false? a segment bc is one - half the length of segment ef. b segment cd is half the length of segment gh. c the length of segment ad is 3 units.

Explanation:

Step1: Find the scale - factor

Since EFGH is a scaled - copy of ABCD, compare corresponding sides. Let's find the scale - factor by comparing two known corresponding sides. For example, if we compare side EH = 10 and side AD (assume AD corresponds to EH), and assume the scale - factor is \(k\). We can also compare GH = 8 and CD = 5. The scale - factor \(k=\frac{EH}{AD}=\frac{GH}{CD}\). From GH = 8 and CD = 5, the scale - factor \(k = \frac{8}{5}=1.6\).

Step2: Analyze option A

EF = 6. If BC is one - half the length of EF, then BC=\(\frac{1}{2}\times6 = 3\). Let's check using the scale - factor. If we assume the correct correspondence, we can find the length of BC from the scale - factor relationship. But if we consider the scale - factor \(k = 1.6\), if we assume a side of ABCD is \(x\) and its corresponding side in EFGH is \(y\), then \(y=kx\).

Step3: Analyze option B

CD = 5 and GH = 8. Since \(\frac{CD}{GH}=\frac{5}{8}=0.5\), segment CD is half the length of segment GH.

Step4: Analyze option C

We know the scale - factor \(k = 1.6\). If EH = 10 and EH corresponds to AD, then \(EH=k\times AD\), so \(AD=\frac{EH}{k}=\frac{10}{1.6}=6.25
eq3\).

Answer:

C. The length of Segment AD is 3 units.