Question

1. which of the following statements is false about rectangle defg? figure 1 options: hf = 7, df = 14, hg = 7, eh = 14

Explanation:

Step1: Recall Rectangle Diagonal Properties

In a rectangle, diagonals are equal and bisect each other. So \( DEFG \) has diagonals \( DF \) and \( EG \), intersecting at \( H \). Thus, \( DH = HF = EH = HG \).

Step2: Analyze Given Length \( DH = 7 \)

From the diagram, \( DH = 7 \). By diagonal properties, \( HF = DH = 7 \), \( HG = DH = 7 \), and \( DF = DH + HF = 7 + 7 = 14 \). But \( EH \) should equal \( DH = 7 \), not \( 14 \).

Step3: Evaluate Each Option

• \( HF = 7 \): True (bisecting diagonals).
• \( DF = 14 \): True (\( 7 + 7 \)).
• \( HG = 7 \): True (bisecting diagonals).
• \( EH = 14 \): False (should be \( 7 \)).

Answer:

EH = 14