How do we say conclusively that the right side of the trapezoid is length 6?
The 2 bases visually seem parallel to each other, and the 2 sides visually seem equal.
The way I found the right side = 6 is a longer method, but I’m sure there’s a rule I’m missing which can get me to do it quicker. What is it?
What I did:
Step 1: I drew the height perpendicular to the bottom base. This forms a 30-60-90 triangle
Step 2: With the 30-60-90 triangle rule, I found the other 2 sides of the triangle.
Step 3: Visually, the 2 triangles look the same size (SSS), because the 2 bases also appear parallel to each other visually. And all have the same angles (AAA).
Step 4: By the size assumption, I concluded that the 2 triangles are congruent. So the right side triangle should also have a hypotenuse of 6; thus making the length of the right side of the trapezoid = 6
Were all the angles given to you? If so, then yes both triangles are congruent by AAS. Alternatively, you can note that the figure is an isosceles trapezoid.
How do we conclude that this is an isosceles trapezoid?
Also, what conclusions can we make about the sides of the trapezoid if it is isosceles?
2,3,4, and 6 are necessary and sufficient conditions
Thanks for this!
What’s the difference between 3 and 5?
We had just these given in the question - the 4 angles and 1 leg side length. Is that sufficient?
The third one tells you that \angle B = \angle C and \angle A = \angle D
The fifth one tells you that \angle B + \angle A = 180 or \angle C + \angle D = 180
That’s basically #3, which is a defining feature of an isosceles trapezoid. If #3 holds true in a trapezoid, then it must be an isosceles trapezoid. Similarly, if the figure in question is an isosceles trapezoid, then it must satisfy #3. It is a biconditional statement, so it works both ways.
Oh gotcha. This helps!
I think we have both 3 and 5 in this question. Yeah the isosceles trapezoid makes a lot of conclusions a lot easier. Thanks!
