Question

In a quadrilateral ABCD, the diagonals intersect at point T. Side AB is parallel and congruent to side DC.

In a quadrilateral ABCD, the diagonals intersect at point T. Side AB is parallel and congruent to side DC.

Answer 1

Based on the given conditions, which statement is presented first to show that segment DT is equal to segment TB?

Answer 2

In these problems, you are supposed to prove that the quadrilateral is a Parallelogram using the diffirent postulates and Theorems provided. FLVS may present some questions that seem difficult at first, but if you review the lesson, most of the questions are closely related to those given in worksheets and assignments.

1. I was stuck on this question for quite some time myself but the best option is to call your Instructor and confront her about not understanding the lesson. For a fact I do know that Response 3 is SAS Congruence Postulate.

2. Quadrilateral ABCD is a parallelogram because the opposite angles of this quadrilateral are equal in measure. In the diagram above, Angle ABC and ADC are 65 degrees and by solving I can identify the measure of Angle DAB and DCB.
180 - 65 = 115 degrees
180 - 65 = 115 degrees
2(115) + 2(65) = 360 degrees
Because the opposite angles of this quadrilateral are equal in measure then this quadrilateral is a parallelogram due to the fact that it supports Theorem 5-9. Theorem 5-9 states that if both pairs of opposite angles in a quadrilateral are congruent, then it is a parallelogram.

3. Quadrilateral ABCD is a parallelogram because the opposite sides of this quadrilateral are congruent. In the diagram above, Segment AB and Segment DC are 7.25 mm while Segment AD and BC are 5.2 mm.
Because the opposite sides of this quadrilateral are congruent then this quadrilateral is a parallelogram due to the fact that it supports Theorem 5-6. Theorem 5-6 states that if both pairs of opposite sides are congruent, then the quadrilateral is a parallelogram.

4. By using the Midpoint Formula, I can deduct that if the midpoints are the same for the diagonals that bisect each other, Parallelogram ABCD supports Theorem 5-7.Theorem 5-7 states that if the diagonals of a quadrilateral bisect each other then it is a parallelogram.
A(-5, -1) and C(4, -3)
Midpoint Formula
(x1 + x2 / 2 , y1 + y2 / 2)
(-5 + 4 / 2 , -1 + (-3)/ 2)
(-1 / 2 , -4 / 2)
(-0.5, -2)
B(6, 1) and D(-7,-5)
Midpoint Formula
(x1 + x2 / 2 , y2 + y1 / 2)
(6 + (-7) / 2 , 1 + (-5)/ 2)
(-1 / 2 , -4 / 2)
(-0.5 , -2)

5. Theorem 5-8 states that if one pair of opposite sides of a quadrilateral is both congruent and parallel, then it is a parallelogram. Using the Slope Formula we can deduct that the opposite sides of the quadrilateral are parallel.
Slope formula:
(y2 - y1) / (x2 - x1)
Line AB slope:
m = (y2 - y1) / (x2 - x1)
m = (1 - (-1)) / (6 - (-5))
m = (1 + 1) / (6 + 5)
m = 2 / 11
Line DC slope:
m = (y2 - y1) / (x2 - x1)
m = (-3 - (-5)) / (4 - (-7))
m = (-3 + 5) / (4 + 7)
m = 2 / 11

Please do me a favor and do not copy and paste these answers directly. Honestly, most people wouldn’t answer these mathematical equations with various details as proof which is what makes my answers different from other students. Try and read the lessons from now on and maybe you will be able to understand more on the information.
Source(s):
The effectiveness of studying and reviewing lessons and examples on the FLVS Geometry lessons.

Answer 3

But which step to prove DT equals TB first?

Answer 4

just try read what post on here so u will no what to do anyway all the answer is there