Question

drag each length to the correct location on the image. each length can be used more than once, but not all lengths will be used
what are the missing segment lengths shown in the image?
10√2 10 20 10√3 20√2 20√3
image of a geometric figure with triangles, angles, and right angles

Explanation:

Answer:

To solve for the missing segment lengths, we analyze the right triangles with \(45^\circ\) angles (isosceles right triangles) and use the properties of such triangles (\( \text{leg} \times \sqrt{2} = \text{hypotenuse} \), or \( \text{hypotenuse} / \sqrt{2} = \text{leg} \)):

Triangle \(ACD\) (Right Isosceles, \( \angle D = 45^\circ \), \( \angle C = 90^\circ \)):

• Hypotenuse \( AD = 20 \).
• Let leg \( AC = x \). For a \( 45^\circ-45^\circ-90^\circ \) triangle, \( x\sqrt{2} = 20 \), so \( x = \frac{20}{\sqrt{2}} = 10\sqrt{2} \). Thus, \( AC = 10\sqrt{2} \), and \( CD = AC = 10\sqrt{2} \) (legs are equal).

Triangle \(ABC\) (Right Isosceles, \( \angle B = 90^\circ \), \( \angle ACB = 45^\circ \)):

• Leg \( AC = 10\sqrt{2} \). Let leg \( AB = BC = y \). For a \( 45^\circ-45^\circ-90^\circ \) triangle, \( y\sqrt{2} = AC = 10\sqrt{2} \), so \( y = 10 \). Thus, \( AB = 10 \) and \( BC = 10 \).

Summary of Missing Lengths:

• \( AC = 10\sqrt{2} \)
• \( CD = 10\sqrt{2} \)
• \( AB = 10 \)
• \( BC = 10 \)

(Note: The exact placement depends on the image’s labeled segments, but the calculations above give the missing lengths using \(45^\circ-45^\circ-90^\circ\) triangle properties.)