Question

Show that squares are the only rectangles with perpendicular diagonals. D C Place a rectangle with sides AB, BC, DC, and AD so that A is located at the origin with vector AB lying on the x-axis. Let AD = BC and AB = DC. Notice that AC and DB are the two vectors representing the diagonals of the rectangle. What must be true if the diagonals are perpendicular?

Name: show that squares are the only rectangles with perpendicular diagonals d c place a rectangle with sides ab bc dc and ad so that a is located at the origin with vector ab lying on the x axis 93926
Uploaded: 2021-08-23T09:10:04-08:00
Duration: 3 min 18 s
Channel: Ayman Sherif
Description: show that squares are the only rectangles with perpendicular diagonals d c place a rectangle with sides ab bc dc and ad so that a is located at the origin with vector ab lying on the x axis 93926

          Show that squares are the only rectangles with perpendicular diagonals.
D
C
Place a rectangle with sides AB, BC, DC, and AD so that A is located at the origin with vector AB lying on the x-axis. Let AD = BC and AB = DC. Notice that AC and DB are the two vectors representing the diagonals of the rectangle. What must be true if the diagonals are perpendicular?

Added by Kelly B.

Geometry A Common Core Curriculum

Ron Larson, Laurie Boswell 1st Edition

Instant Answer

Solved by Expert Ayman Sherif

08/23/2021

Step 1

Let vector \(\overrightarrow{AB}\) lie along the x-axis. - Let the length of \(\overrightarrow{AB}\) be \(w\). So, \(B = (w, 0)\). - Let the length of \(\overrightarrow{AD}\) be \(h\). So, \(D = (0, h)\). - Since \(ABCD\) is a rectangle, \(C\) is at \((w, Show more…

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Show that squares are the only rectangles with perpendicular diagonals. D C Place a rectangle with sides AB, BC, DC, and AD so that A is located at the origin with vector AB lying on the x-axis. Let AD = BC and AB = DC. Notice that AC and DB are the two vectors representing the diagonals of the rectangle. What must be true if the diagonals are perpendicular?