Question

question 4 of 5

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?

Explanation:

Analyze triangle ABC

Using the Isosceles Right Triangle and Special Right Triangles knowledge points:
In \(\triangle ABC\), we have:

• \(\angle C = 45^\circ\)
• \(\angle ABC = 90^\circ\)
• \(\angle CAB = 180^\circ - 90^\circ - 45^\circ = 45^\circ\)
• Hypotenuse \(AC = 14\sqrt{2}\)

Since \(\triangle ABC\) is a \(45^\circ-45^\circ-90^\circ\) triangle, the legs \(AB\) and \(BC\) are equal:

$$ AB = BC = \frac{AC}{\sqrt{2}} = \frac{14\sqrt{2}}{\sqrt{2}} = 14 $$

Analyze triangle ABD

Using the Isosceles Right Triangle and Special Right Triangles knowledge points:
In \(\triangle ABD\), we have:

• \(\angle ADB = 90^\circ\)
• \(\angle DAB = 45^\circ\)
• \(\angle ABD = 180^\circ - 90^\circ - 45^\circ = 45^\circ\)
• Hypotenuse \(AB = 14\)

Since \(\triangle ABD\) is a \(45^\circ-45^\circ-90^\circ\) triangle, the legs \(AD\) and \(BD\) are equal:

$$ AD = BD = \frac{AB}{\sqrt{2}} = \frac{14}{\sqrt{2}} = 7\sqrt{2} $$

Answer:

• Segment \(AB\) (middle-left box): <blank>\(14\)</blank>
• Segment \(BC\) (bottom-left box): <blank>\(14\)</blank>
• Segment \(AD\) (top-right box): <blank>\(7\sqrt{2}\)</blank>
• Segment \(BD\) (bottom-right box): <blank>\(7\sqrt{2}\)</blank>