A trapezoid has ONLY ONE set of parallel sides. When proving a figure is a trapezoid, it is necessary to prove that two sides are parallel and two sides are NOT parallel.

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The angles on the same side of a leg are called adjacent angles such as ∠A and ∠D are supplementary. For the same reason, ∠B and ∠C are supplementary.

The midsegment of a trapezoid is:parallel to both baseshas length equal to the average of the length of the bases

The median (also called the mid-segment) of a trapezoid is a segment that connects the midpoint of one leg to the midpoint of the other leg.

The median (or mid-segment) of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.(True for ALL trapezoids.)

1. A trapezoid is isosceles if and only if the base angles are congruent. 2. A trapezoid is isosceles if and only if the diagonals are congruent. 3. If a trapezoid is isosceles, the opposite angles are supplementary. Never assume that a trapezoid is isosceles unless you are given (or can prove) that information.

Bases - The two parallel lines are called the basesThe Legs - The two non parallel lines are the legs.

I have:1. only one set of parallel sides2. base angles congruent3. legs congruent4. diagonals congruent5. opposite angles supplementary

First, let us make the trapezoid. You start with a triangle of sides a, b, and c where the sides a and b meet to form a right angle. Then put a second triangle below the first such that side a is an extension of the other triangles b side.

Second, put a second triangle below the first such that side a is an extension of the other triangles b side.

To find the length of the diagonal, we need to use the pythagorean Theorem. Therefore, we need to sketch the following triangle within the trapezoid: ABCD

we know that the base of the triangle has length of 9 m. By subtracting the top the trapezoid from the bottom of the trapezoid, we get:12 m - 6 m = 6 mDividing by two, we have the length of each additional side on the bottom of the trapezoid. 6m/2 = 3madding these two values together, we get 9 m .The formula for the length of the diagonal AC uses the Pythagorean Theorem:AC2 = AE 2 + EC2, where E is the point between a and D representing the base of the triangle.AC2 = (9m)2 + (4 m)2AC2 = square of 97 m

In trapezoid ABCD:(1) The degree measure of the four angles add up to 360 degrees. This is actually true of any quadrilateral. Let lower case letters a, b, c and d = the angles of trapezoid ABCD.Then: a + b + c + d = 360 degrees.

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(2) The corresponding pairs of base angles, such as A and B, or C and D, are supplementary (add up to 180 degrees).angle a + angle b = 180 degrees angle c + angle d = 180 degrees

A trapezoid is isosceles if and only if the base angles are congruent. Given : ABCD is an isosceles trapezoid. AD ≅ BC and AB || CD.Prove that : ∠C ≅ ∠D

We are going to show that the diagonals of an isosceles trapezoid are congruent. In the figure below, we will show that AC is congruent to BD.