Geometry help please?

1) Parallelogram ACFD is split in two parts so that ABED and FEBC are congruent isosceles trapezoids. What are the measures of all the angles of trapezoid FEBC if angle D is 48°?

Shows parallelogram A C F E split by segment B E making two congruent isosceles trapezoids. Angle D equals 48 degrees.

Angle C = _________________

Angle F = _________________ (Hint: Angle A is congruent to Angle F)

Angle <CBE = ________________

Angle <FEB = ________________

2) Two congruent "door-stop" trapezoids are placed edge-to-edge with measurements and markings as shown. Find the length of segment AC.

Two congruent door stop trapezoids are shown. Trapezoid ABED and Trapezoid CBEF share side BE. Side BE is congruent to side AB and CB. The hypotenuse of triangle BEF is 25 cm. The base of triangle BEF is 20 cm.

3) A kite has diagonals of 18 inches and 21 inches as seen below. What is the perimeter of the kite?

Shows a kite with short diagonal of 18 divided 9 and 9, longer diagonal of 21 divided 9 and 12

1 Answer

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    1) Angle C=48

    Angle F=132

    Angle <CBE =48

    Angle <FEB =132

    2) BE=(25)^2- (20)^2=625-400=225

    BE=15

    AB=CB=BE=15

    AC=15+15=30

    3)Use the Pythagorean Thm to find the sides

    The smaller side a is

    (9)^2+(9)^2=162

    a=sqrt(192)=12.73 approx.

    The larger side b is

    (12)^2+(9)^2=225

    b=sqrt(225)=15

    The perimeter is 12.73+12.73+15+15=55.46

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