math

Let (AB) and (CD) be 2 parallel lines by a transversal at E and F respectively.The bisector of AEF and BEF cut (CD) at M and N respectively.The bisector of CFE cuts [ME] at S, and the bisector of DFE cuts [Ne] at T.Show that: ETFS is a rectangle

  1. 👍 0
  2. 👎 0
  3. 👁 186
  1. The sum of angles AEF and BEF is 180 degrees. Therefore the sum of the bisectors of those angles (MEF and FEN) is 90 degrees. That sum angle (MEN or SET) is one of the angles of quadrilateral SETF. Angles BEF and EFM are equal because of the way EF intercpts parallel lines. Therefore EN and SF are parallel. SE and FT are parallel for the same reason.

    Therefore EFTS is a parallelogram. Since we have shown it has one right angle, all angles are right angles, so it is a rectangle.

    You will have to draw the figure, as I did, to make sense of all that.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    In the diagram, transversal GH intersects parallel lines AB amd CD. m

    asked by me on January 16, 2013
  2. Geometry

    Examine the two distinct lines defined by the following two equations in slope-intercept form. line ℓ: y=34x+6 line k: y=34x−7 Are lines ℓ and k parallel? Justify your response. 1.Yes, lines ℓ and k are parallel because

    asked by Anonymous on June 9, 2020
  3. Geometry

    Line ℓ contains the points A(2,2) and B(3,6). Line k contains the points C(0,5) and D(1,9). Yes, lines ℓ and k are parallel because the lines pass through the same points. No, lines ℓ and k are not parallel because the

    asked by Anonymous on June 9, 2020
  4. Math

    1. is line "L" parallel to line "M"? *picture of a transversal.. lines L and M don't touch and one line crosses through line L and M to create a transversal. angles 124 and 118 are on the bottom left side of the transversal* I

    asked by ash on January 27, 2015
  5. Geometry

    For every 10 yards on a football field, there is a boldly marked line labeled with the amount of yards. There are two parallel sidelines on each side of the field. If the 50 yard line is perpendicular to one of the sidelines, what

    asked by Anonymous on September 17, 2018
  1. maths

    if two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2:3,then the smaller of two angles is

    asked by sakina on July 8, 2011
  2. Maths

    To parallel lines l and m are cut by transversal t if the interior angles of the same side of t be (2x-8) and (3x-7) find the measure of each of these angles

    asked by Shehzad on June 28, 2017
  3. Math

    A transversal intersects two lines. Which conditions would always make the two lines parallel? A) Vertical Angles are Congruent B) Alternate interior angles are congruent C) Corresponding angles are supplementary D) Same-side

    asked by Joseph on October 10, 2018
  4. geometry

    Martin drew a pair of perpendicular lines and a pair of parallel lines. Which of these statements best compares the pairs of perpendicular and parallel lines? Answer A: Perpendicular and parallel lines always have a common

    asked by Sam on September 25, 2011
  5. math

    Two parallel lines cut by a transversal can create all the following types of angles except

    asked by sabrina on January 3, 2010
  6. MATH HELP

    A consistent system of equations is a system with __________. the same line parallel lines intersecting lines and lines that have the same slope intersecting lines and lines that have the same equation

    asked by Oscar on September 10, 2015

You can view more similar questions or ask a new question.