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Find Length of Segment CD with AB=21, BC=14, AD=54
Mathematics
Grade 8 (Junior High School)
Question Content
In the figure, it is given that AB = 21, BC = 14, and AD = 54. Find the length of CD.
Correct Answer
19
Detailed Solution Steps
1
Step 1: Identify that points A, B, C, D are collinear (implied by the sequential segment notation), so the total length AD is equal to the sum of AB, BC, and CD.
2
Step 2: Rearrange the segment addition formula to solve for CD: CD = AD - AB - BC.
3
Step 3: Substitute the given values: CD = 54 - 21 - 14 = 19.
Knowledge Points Involved
1
Multi-Segment Addition Postulate
For four collinear points A, B, C, D in sequence, the total length of segment AD is equal to the sum of the lengths of AB, BC, and CD (AD = AB + BC + CD). This extends the basic segment addition postulate to more than three collinear points, used to find unknown segments in a long collinear sequence.
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