Question

grade 7 unit 1: end - of - unit assessment (a)
you will need a centimeter ruler for the problem in which you draw a bedroom floor plan.

1. quadrilateral efgh is a scaled copy of quadrilateral abcd. select all of the true statements.

a. segment ef is twice as long as segment ab.
b. segment cd is twice as long as segment fg.
c. the measure of angle hef is twice the measure of angle dab.
d. the length of segment eh is 16 units.
e. the area of efgh is twice the area of abcd.

Explanation:

Step1: Find the scale factor

Since \(CD = 6\) and \(GH=12\), the scale factor \(k=\frac{GH}{CD}=\frac{12}{6} = 2\)

Step2: Analyze each option

• Option A:

\(AB = 3\), \(EF=(3 + 4)\times2=14\) (incorrect)

• Option B:

\(CD = 6\), \(FG = 4\times2 = 8\) (incorrect)

• Option C:

In scaled - copies, corresponding angles are equal. \(\angle HEF=\angle DAB\) (incorrect)

• Option D:

\(AD = 8\), \(EH=8\times2=16\) (correct)

• Option E:

If the scale factor is \(k = 2\), the area scale factor is \(k^{2}=4\). Area of \(EFGH\) is \(4\) times the area of \(ABCD\) (incorrect)

Answer:

D. The length of segment \(EH\) is \(16\) units.