Question

1. which of the following statements is false about rectangle defg?

figure 1

• hg = 7
• df = 14
• eh = 14
• hf = 7

Explanation:

⚡ Using what you learned: properties of quadrilaterals

Step 1: Identify given values

From the image, we are given:

• \( DEFG \) is a rectangle.
• The top side \( EF = 5 \).
• The segment \( DH = 7 \), where \( H \) is the intersection point of the diagonals \( DF \) and \( EG \).

Step 2: Apply diagonal properties of a rectangle

In a rectangle, the diagonals are equal in length and bisect each other. This means:

$$ EG = DF $$

$$ DH = HF = \frac{1}{2} DF $$

$$ EH = HG = \frac{1}{2} EG $$

Since all four half-diagonals are equal:

$$ DH = HF = EH = HG = 7 $$

Step 3: Calculate full diagonal lengths

Using the half-diagonal length:

$$ DF = DH + HF = 7 + 7 = 14 $$

$$ EG = EH + HG = 7 + 7 = 14 $$

Step 4: Evaluate the options

• \( HG = 7 \) (True, since \( HG = DH = 7 \))
• \( DF = 14 \) (True, since \( DF = 2 \times DH = 14 \))
• \( EH = 14 \) (False, since \( EH = DH = 7 \))
• \( HF = 7 \) (True, since \( HF = DH = 7 \))

The false statement is \( EH = 14 \).

Answer:

\( EH = 14 \)