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Grades 11-12 Video Solutions 2024
2024_11-12_13
2024_11-12_13
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Video Transcription
A quadrilateral ABCD has two right angles at B and C, where AB equals 4, BC equals 8, and CD equals 2. Point X lies on BC. What is the minimum possible value of AX plus DX? We extend line AB through X to point Y, such that AB equals BY. We note that ABX and YBX will be congruent, so AX will be equal to XY. We can also extend DX to then meet Y, and since DY is DX plus XY, and that's also DX plus AX, then it is the minimum possible length. Thus, we can use the Pythagorean theorem to find that the minimum possible length is 10.
Video Summary
A quadrilateral ABCD has two right angles at B and C, where AB equals 4, BC equals 8, and CD equals 2. Point X lies on BC. What is the minimum possible value of AX plus DX? We extend line AB through X to point Y, such that AB equals BY. We note that ABX and YBX will be congruent, so AX will be equal to XY. We can also extend DX to then meet Y, and since DY is DX plus XY, and that's also DX plus AX, then it is the minimum possible length. Thus, we can use the Pythagorean theorem to find that the minimum possible length is 10.
Keywords
quadrilateral
Pythagorean theorem
minimum length
congruent triangles
geometry problem
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