Trapezoids
What is true about the angles of an isosceles trapezoid?
Base angles are equally (The top two angles are equal and the bottom two angles are equal)
Given the diagram on card D, what is the relationship of w,x,y, and z?
xy=zw
Given the diagram on card E, what is the relationship of A, B, C?
A = 1/2(C-B)
What is a proof?
A logical argument that shows there is no other option.
Two lines cut by a transversal are parallel if and only if.....?
Alternate interior angles are congruent, corresponding angles are congruent, and same side interior angles are supplementary.
What relationship does the median of a trapezoid have to its bases?
It is the average of both.
Given the diagram on card E, what is the relationship of w,x,y, and z?
(x+w)w = (z+y)y
Given the diagram on card D, what is the relationship of A, B, and C
What is a proof by contradiction?
A proof where you negate the statement you are proving and show that it contradicts reality.
Given two sides of a quadrilateral are both equal and parallel, do we know the shape is a parallelogram? How?
Yes, using parallel angle congruencies and congruent triangles.
What is the sum of the interior angles of a trapezoid?
360
Given the diagram on card B, what is the value of x?
12
Given the diagram on card C, what is the value of y?
15 degrees
Is the following logically correct? If not, Why?
If two triangles are congruent, then their corresponding angles are congruent. Triangle ABC equals triangle XYZ therefore angle A equals angle X.
Yes
Given a parallelogram, what must be true for it to be a square.
All sides must be equal and the angles must right angles.
The bases of a trapezoid are 7 inches and 23 inches, how long is the median?
15 inches
Given the diagram on card C, what is the value of x?
9
Given the diagram on card A, what is the value of y?
15 degrees
Is the following logically correct? If not, Why?
If two lines are parallel, then their alternate interior angles are congruent. Line AB and CD have congruent alternate interior angles, therefore they are parallel.
No, you assumed the conclusion implies the premises.
Given the length of the diagonals of a parallelograms, what must be true for you to be able to calculate the lengths of the sides?
The angles must be right.
If a base and the median are 4 inches and 10 inches respectfully. How long is the second base?
16 inches
Given the diagram on card A, what is the value of x?
The square root of 55
Given the diagram on card B, what is the value of y?
30 degrees
If you are proving that two lines cut by a transverse are not parallel, why can't you use triangle propositions?
It would be assuming the conclusion.
If two parallel lines are cut by two transversal, how many distinct angles are there? (ie. how many angles with different measurements are there?)
4