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Trapezoid ABCD has parallel sides AB and CD, of lengths a and b respectively. Diagonals AC and BD intersect at E. Draw the line through E that is parallel to AB and CD, and let P and Q be its intersections with AD and BC respectively. (a) Prove that E is the midpoint of PQ. (b) Show that PQ=1/[1/2(1/a + 1/b)] . PQ is known as the harmonic mean of a & b.

Trapezoid ABCD has parallel sides AB and CD, of lengths a and b respectively. Diagonals AC and BD intersect at E. Draw the line through E that is parallel to AB and CD, and let P and Q be its intersections with AD and BC respectively. (a) Prove that E is the midpoint of PQ. (b) Show that PQ=1/[1/2(1/a + 1/b)] . PQ is known as the harmonic mean of a & b.

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter85: Hexadecimal Numeration System
Section: Chapter Questions
Problem 5A
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  1. Trapezoid ABCD has parallel sides AB and CD, of lengths a and b respectively. Diagonals AC and BD intersect at E. Draw the line through E that is parallel to AB and CD, and let P and Q be its intersections with AD and BC respectively.

(a) Prove that E is the midpoint of PQ.

(b) Show that PQ=1/[1/2(1/a + 1/b)] . PQ is known as the harmonic mean of a & b.

890. Trapezoid ABCD has parallel sides AB and CD, of lengths a and b respectively. Diag- onals AC and BD intersect at E. Draw the line through E that is parallel to AB and CD, and let P and Q be its intersections with AD and BC respectively. (a) Prove that E is the midpoint of PQ. 1 (b) Show that PQ = 1/2 ( 1²1 + 1 ) PQ is known as the harmonic mean of a and b.
Transcribed Image Text:890. Trapezoid ABCD has parallel sides AB and CD, of lengths a and b respectively. Diag- onals AC and BD intersect at E. Draw the line through E that is parallel to AB and CD, and let P and Q be its intersections with AD and BC respectively. (a) Prove that E is the midpoint of PQ. 1 (b) Show that PQ = 1/2 ( 1²1 + 1 ) PQ is known as the harmonic mean of a and b.
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