1. Questions

Math

In rhombus DEFG, if m<DEF=60, and the shorter diagonal DF has a length of 7, find the length of the side of a rhombus.

  1. 👍
  2. 👎
  3. 👁
Chris

  1. In a rhombus, the diagonals right-bisect each other.
    I recognize the 30-60-90 triangle in the diagram.
    then
    x/2 = 3.5/1
    x = 7
    (sure enough, triangle DEF is equilateral)

    1. 👍
    2. 👎
    Reiny

  2. So one side of the rhombus is equal to seven? I'm still confused as to how you got your answer...

    1. 👍
    2. 👎
    Chris

  4. Ok, I will use a different approach this time.

    Hope you make a sketch.
    Since one angle is 60º, then its opposite angle is also 60º, properties of a parallelogram.
    Which means the other angle pair is 120º each, (angle D = angle F = 120)
    Now look at your diagram, don't you see two equilateral triangles,
    triange DEF and also triangle DGF.
    So all sides in those two triangles must be equal,
    since DF = 7 , the sides of the rhomubus are 7 each.

    1. 👍
    2. 👎
    Reiny

  5. I see it now,because a diagonal divides a parallelogram into two congruent triangles! Thank you!!

    1. 👍
    2. 👎
    Chris

Respond to this Question

First Name

Your Response

Similar Questions

  1. Geometry

    10. Which of the following quadrilaterals always have diagonals that are congruent. Circle all that apply Parallelograms Rectangles Rhombi Squares Isosceles trapezoids 19. Given square ABCD: if the measure of angle ACB = (1x - 32)

  2. math

    Diagonal of a rhombus are in the ratio 3:4. If its perimeter is 40cm, find the length of the side and diagonals of rhombus

  3. geometry

    In the diagram below of isosceles trapezoid DEFG, DE ll GF. DE = 4x − 2, EF = 3x + 2, FG = 5x − 3, and GD = 2x + 5. Find the value of x. the answer is 3 but idk how, please help

  4. geometry

    The coordinates for a rhombus are given as (2a, 0), (0, 2b), (–2a, 0), and (0, –2b). Write a plan to prove that the midpoints of the sides of a rhombus determine a rectangle using coordinate geometry. Be sure to include the

  1. Geometry

    10. Which of the following quadrilaterals always have diagonals that are congruent. Circle all that apply Parallelograms Rectangles Rhombi Squares Isosceles trapezoids 19. Given square ABCD: if the measure of angle ACB = (1x - 32)

  2. geometry

    the lengths of the diagonal of a rhombus are 2 in and 5 in. find the measure of the angles of the rhombus to the nearest degree. if it helps, we are learning how to use tangent right now!

  3. Math

    Which of the following statements is not always true? A. In a rhombus, the diagonals bisect opposite angles. B. In a rhombus, the diagonals are perpendicular. C. In a rhombus, the diagonals are congruent. D. In a rhombus, all four

  4. Geometry

    A rhombus has diagonals of length 4 and 10. Find the angles of the rhombus to the nearest degree. would the angles be 136 and 44?

  1. MATH

    Name the quadrilaterals that have four equal angles. A. rhombus, square B. Square, rectangle C. parallelogram, rhombus D. rhombus, trapezoid My answer B

  2. Geometry

    Two sides of a rhombus form a 120º angle. The length of each side is 6 in. Explain how to find the area of the rhombus, and then calculate the area. Leave your answer in simplest radical form.

  3. math

    The area of a rhombus is 139.2cm.cm.and its altitude is 9.6cm.find the perimeter of the rhombus?

  4. geometry

    In the rhombus ABCD, AB=10 and AC=12. Find the area of the rhombus. I am confused about how to solve this problem.

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