Question

you will need a centimeter ruler for the problem in which you draw a kitchen floor plan. problem 1 quadrilateral abcd is a scaled copy of quadrilateral efgh. select all of the true statements. a. segment bc is half the length of segment ef. b. segment cd is half the length of segment gh. c. the measure of angle adc is equal to the measure of angle ehg d. the length of segment ab is 3 units. e. the area of abcd is half the area of efgh.

Explanation:

Step1: Recall properties of scaled - copies

In scaled - copies, corresponding angles are equal and corresponding side - lengths are in proportion.

Step2: Analyze option A

There is no information to suggest that segment $BC$ and segment $EF$ are corresponding segments, so we cannot say segment $BC$ is half the length of segment $EF$.

Step3: Analyze option B

If $ABCD$ is a scaled - copy of $EFGH$, and assuming the scale factor is $\frac{1}{2}$, and $CD$ and $GH$ are corresponding segments, then segment $CD$ is half the length of segment $GH$.

Step4: Analyze option C

Since $ABCD$ is a scaled - copy of $EFGH$, corresponding angles are equal. $\angle ADC$ and $\angle EHG$ are corresponding angles, so the measure of angle $ADC$ is equal to the measure of angle $EHG$.

Step5: Analyze option D

There is no information given about the length of segment $AB$ being 3 units.

Step6: Analyze option E

If the scale factor of the side - lengths of two similar figures (scaled copies) is $k$, the ratio of their areas is $k^{2}$. If $k=\frac{1}{2}$, the area of $ABCD$ is $\frac{1}{4}$ of the area of $EFGH$, not half.

Answer:

B. Segment $CD$ is half the length of segment $GH$.
C. The measure of angle $ADC$ is equal to the measure of angle $EHG$.