A trapezoid has ONLY ONE set of parallel sides. When proving a figure is a trapezoid, that is crucial to prove that 2 sides room parallel and also two sides are NOT parallel.

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The angles on the exact same side of a leg are called surrounding angles such together ∠A and ∠D are supplementary. For the very same reason, ∠B and ∠C space supplementary.
The midsegment the a trapezoid is:parallel to both baseshas length equal come the mean of the size of the bases
The average (also dubbed the mid-segment) the a trapezoid is a segment the connects the midpoint that one foot to the midpoint of the various other leg.
The mean (or mid-segment) of a trapezoid is parallel to every base and also its size is one fifty percent the sum of the lengths the the bases.(True for every trapezoids.)
1. A trapezoid is isosceles if and only if the basic angles room 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 provided (or have the right to prove) the information.
Bases - The two parallel present are referred to as the basesThe legs - The two non parallel lines are the legs.
I have:1. Just one collection of parallel sides2. Base angle congruent3. Legs congruent4. Diagonals congruent5. Opposite angle supplementary
First, let united state make the trapezoid. You begin with a triangle of political parties a, b, and also c wherein the political parties a and also b fulfill to kind a right angle. Then put a second triangle listed below the an initial such the side a is an expansion of the other triangles b side.
Second, placed a 2nd triangle below the very first such the side a is an expansion of the various other triangles b side.
To find the length of the diagonal, we should use the pythagorean Theorem. Therefore, we must sketch the adhering to triangle in ~ the trapezoid: ABCD
we understand that the base of the triangle has length of 9 m. By individually the peak the trapezoid indigenous the bottom of the trapezoid, we get:12 m - 6 m = 6 mDividing by two, we have actually the size of each added side on the bottom of the trapezoid. 6m/2 = 3madding these two values together, we get 9 m .The formula because that the length of the diagonal line AC offers the Pythagorean Theorem:AC2 = AE 2 + EC2, whereby E is the suggest between a and also D representing the basic of the triangle.AC2 = (9m)2 + (4 m)2AC2 = square the 97 m
In trapezoid ABCD:(1) The degree measure of the 4 angles add up come 360 degrees. This is in reality true of any type of quadrilateral. Let lower instance letters a, b, c and d = the angle of trapezoid ABCD.Then: a + b + c + d = 360 degrees.

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(2) The equivalent pairs of base angles, such together A and B, or C and D, are supplementary (add approximately 180 degrees).angle a + angle b = 180 degrees angle c + angle d = 180 degrees
A trapezoid is isosceles if and also only if the base angles space congruent. Given : ABCD is one isosceles trapezoid. Ad ≅ BC and abdominal || CD.Prove the : ∠C ≅ ∠D
We space going to display that the diagonals of an isosceles trapezoid space congruent. In the figure below, we will show that AC is congruent to BD.    