Question

quadrilateral efgh is a scaled copy of quadrilateral abcd. which of the following statements is false? a segment cd is half the length of segment gh. b segment bc is one - half the length of segment ef. c the measure of angle adc is equal to the measure of angle ehg. d the length of segment ab is 3 units.

Explanation:

Step1: Recall properties of scaled - copies

Scaled - copies have proportional side - lengths and equal corresponding angles.

Step2: Analyze side - length ratios

Let's assume the scale factor from quadrilateral \(ABCD\) to \(EFGH\) is \(k\). If we consider the vertical sides \(AD = 5\) and \(EH=10\), the scale factor \(k = 2\).

Step3: Check option A

If the scale factor is \(2\), and for corresponding sides \(CD\) and \(GH\), segment \(CD\) is half the length of segment \(GH\) since \(\frac{CD}{GH}=\frac{1}{k}\), so option A is true.

Step4: Check option B

There is no information given about the lengths of \(BC\) and \(EF\) in the problem - statement to establish a \(\frac{1}{2}\) ratio. But if we assume the scale - factor relationship holds for all corresponding sides, and since the scale factor \(k = 2\), segment \(BC\) should be half the length of segment \(EF\) if they are corresponding sides. However, we need to analyze all options.

Step5: Check option C

Corresponding angles in scaled - copies are equal. \(\angle ADC\) and \(\angle EHG\) are corresponding angles, so \(\angle ADC=\angle EHG\), and option C is true.

Step6: Check option D

If the scale factor \(k = 2\) and \(EF = 6\), and assuming \(AB\) and \(EF\) are corresponding sides (since no other information about non - vertical sides is given and based on the nature of scaled copies), then \(AB=\frac{EF}{2}=3\). So option D is true.

Since we have no information about the relationship between \(BC\) and \(EF\) to confirm the \(\frac{1}{2}\) ratio as stated in option B, and all other options can be verified with the properties of scaled copies, option B is the false statement.

Answer:

B. Segment \(BC\) is one half the length of Segment \(EF\)