Math Proof: Can Someone help!

[mathilliterate]

I had a similar problem last night, i just don't understand how i'm supposed to set these up?

If a diagonal of a parallelogram bisects an angle of the parellelogram, the parallelogram is a rhombus. (state your plan and give your proof)

Given: ABCD is a parallelogram with angle 1 = angle 2
To Prove: ABCD is a rhombus
Plan:__________________________________________

Picture a Rhombus top left corner is point D top right id C bottom left is A bottom Right is B. A line goes from point C to point A, at point A on that line is angle 1 at the top and angle 2 at the bottom. at the top of the line angle 3

Statements: Proof: Reasons:
____________________________________________________________________

 

[wjm11]

If a diagonal of a parallelogram bisects an angle of the parellelogram, the parallelogram is a rhombus. (state your plan and give your proof)[quote]

Ask yourself what things you know about parallelograms:  Their opposing sides are parallel by definition.

The diagonal is a transverse line through two sets of parallel lines, so you can use “alternate interior angles” to show congruency of angles at opposite corners of the parallelogram.  

The diagonal also cuts the parallelogram into two triangles that share a common side (the diagonal).  You can now use SAS (side-angle-side) to show the two triangles are congruent.  By CPCTC (corresponding sides of congruent triangles are congruent)  and isosceles triangle theorems, you can demonstrate that all sides of the parallelogram are congruent.  QED.

 

[mathilliterate]

?

huh? :shock:

 

[tkhunny]

diagonal
parallelogram
bisects
angle
parellelogram
rhombus
proof
parallel
definition.
transverse
line
two
sets
alternate interior angles
congruency
corners
triangles
SAS (side-angle-side)
CPCTC (corresponding sides of congruent triangles are congruent)
isosceles triangle theorem
QED

Aren't those math terms? Why would someone named "mathilleterate" understand them?

 

[stapel]

Ask yourself what things you know about parallelograms...

huh?

Have you not studied parallelograms yet?

Thank you.

Eliz.

 

[mathilliterate]

yes i have but the question wants me to prove that it is a rhombus?

 

[skeeter]

well ... a rhombus is just a parallelogram with all sides congruent.

you should already know that the opposite sides of a parallelogram are congruent ... you just need to show that its adjacent sides are congruent.

hint: a triangle with equal base angles is isosceles ... sides opposite the equal base angles are congruent.