Proving Parallelogram PQRS & Quadrilateral ABCD: Help Needed

In summary: A (\Delta TSR). But that's beside the point. The point is, the question is wrong. And if you can't understand why I say it's wrong, you'll have to post the question exactly as it was given to you. You're right. The question was wrong. It's supposed to be this:1) PQRS is a parallelogram and T is any point inside the parallelogram. Prove that triangle TSR + triangle TQP = parallelogram PQRS2) ABCD is a quadrilateral whose area is bisected by the diagonal AC. Prove that BD is bisected by ACSorry for the confusionIn summary, the conversation discusses two parallelogram proofs
  • #1
ruud
14
0
I'm having trouble with two parallelogram proofs

1) PQRS is a parallelogram and T is any point inside the parallelogram. Prove that triangle TSR + triangle TQP = 1/2 parallelogram PQRS

2) ABCD is a quadrilateral whose area is bisected by the diagonal AC. Prove that BD is bisected by AC

I'm stuck on both of them I know that I need to use the Parallel Area Property but I'm unclear or properties of parallelograms. ANy help will be appreciated
 
Mathematics news on Phys.org
  • #2
You don't need properties of parallelograms. You just need area formulae.
 
  • #3
Could you please explain further
 
  • #4
Tell us what you've done so far.
 
  • #5
First of all, you have stated the problems incorrectly. The problem can't possibly say "Prove that triangle TSR + triangle TQP = 1/2 parallelogram PQRS" because you can't "add" triangles, you can't divide a parallelgram by 2, and two triangles are NOT the same as a parallelgram.

You can, of course, add numbers and divide a number by 2. I'm feel sure that the problem really asked you to show that the sum of the areas of the two triangles is the same as 1/2 the area of the parallelogram. That was why Hurkyl said you need area formulas. Hint: think "base" and "altitude".

"2) ABCD is a quadrilateral whose area is bisected by the diagonal AC. Prove that BD is bisected by AC"

Wow, I hate the wording of that!(And I recognise that it might actually be the way it is worded in your book.) "Area" is a number and cannot be "bisected"! What is meant here is that the diagonal AC divides ABCD into two triangles which each have the same area.
You refer to the "parallelogram area property" but say that you are unsure about the properties. How about quoting the exact statement of the "parallelogram area property" for us? (And once again, think about the formula for area of a triangle. What about two triangles that have the same base and area?)
 
  • #6
He probably meant 'triangle' as in:

[tex]\Delta TSR + \Delta TQP[/tex]

Which means area
 
  • #7
Actually, no, [itex]\Delta TSR[/itex] usually means "triangle TSR". To ask for area symbolicaly, you usually prefix it with m, A, or alpha (or even the whole word "Area"), as in [itex]\alpha (\Delta TSR)[/itex]
 
Last edited:

1. How do you prove that a quadrilateral is a parallelogram?

To prove that a quadrilateral is a parallelogram, you need to show that both pairs of opposite sides are parallel. This can be done by using the properties of parallel lines, such as the alternate interior angles, corresponding angles, or consecutive interior angles theorem.

2. What is the difference between a quadrilateral and a parallelogram?

A quadrilateral is a general term for any four-sided polygon, while a parallelogram is a specific type of quadrilateral with two pairs of parallel sides. In other words, all parallelograms are quadrilaterals, but not all quadrilaterals are parallelograms.

3. Can a quadrilateral be both a parallelogram and a rectangle?

Yes, a rectangle is a special type of parallelogram where all angles are right angles. So, a quadrilateral can be both a parallelogram and a rectangle if it has two pairs of parallel sides and four right angles.

4. How many ways can you prove that a quadrilateral is a parallelogram?

There are several ways to prove that a quadrilateral is a parallelogram, including using the properties of parallel lines, the definition of a parallelogram, or the diagonals of a parallelogram. You can also prove it by showing that both pairs of opposite sides are congruent and parallel.

5. Can you prove that a quadrilateral is a parallelogram if you are given the coordinates of its vertices?

Yes, you can use coordinate geometry to prove that a quadrilateral is a parallelogram. You can do this by showing that the slopes of the opposite sides are equal, or by using the distance formula to show that the opposite sides are congruent.

Similar threads

MHB Need help with parallelogram proof
    • General Math
Replies
1
Views
724
MHB Proof of Parallelogram ABCD: Midpoint X & Y Show Area $\frac{1}{4}$
    • General Math
Replies
5
Views
2K
MHB Prove Equal Area Triangle & Parallelogram, $\angle ADC=90^{\circ}$
    • General Math
Replies
9
Views
3K
Understanding the Parallelogram Area Formula: A Quest for Proof
    • General Math
Replies
9
Views
3K
Proving a parallelogram is a rhombus, given an Isosceles triangle
    • Precalculus Mathematics Homework Help
Replies
16
Views
3K
Vector algebra (proving you have a parallelogram by using vectors)
    • Precalculus Mathematics Homework Help
Replies
7
Views
3K
To find the center of gravity of a particular quadrilateral
    • Introductory Physics Homework Help
Replies
12
Views
2K
Proving Quadrilateral PQRS is a Parallelogram
    • Precalculus Mathematics Homework Help
Replies
7
Views
2K
What are the properties of parallelograms regarding diagonals?
    • General Math
Replies
4
Views
21K
Vectors (prove a quadrilateral is a parallelogram)
    • Calculus and Beyond Homework Help
Replies
2
Views
17K

Hot Threads

Recent Insights

Back
Top