Geometry Proofs (2 Viewers)

[Smile12345]

I'm really not sure about how to do this one... Could someone help me please?

Diagram:

Given Info: AB and BC are straight lines. XBZY is a parallelogram. ZC = ZY and AX = BX. The points A, Y and C are collinear.

a) Prove that Triangle AXY is congruent to Triangle CYZ... - What proof should I use?
b) Prove that XBZY is a rhombus....

Thanks for all your help in advance.

 

[Carrotsticks]

I'm really not sure about how to do this one... Could someone help me please?

Diagram: View attachment 28361

Given Info: AB and BC are straight lines. XBZY is a parallelogram. ZC = ZY and AX = BX. The points A, Y and C are collinear.

a) Prove that Triangle AZY is congruent to Triangle CYZ... - What proof should I use?
b) Prove that XBZY is a rhombus....

Thanks for all your help in advance.

Can you please confirm that (a) was typed correctly?

 

[Smile12345]

Can you please confirm that (a) was typed correctly?

Sorry a) was typed incorrectly... Please forgive me... I've changed it now ( It should be: Prove that Triangle AXY is congruent to Triangle CYZ...)

 

[Carrotsticks]

Is it given that X lies on AB?

 

[Smile12345]

Is it given that X lies on AB?

Yes it is... Sorry my diagram isn't clear...

X is the midpoint between A and B.. .

 

[Carrotsticks]

 

[Carrotsticks]

Oops, the green kinda came out funky. But it's meant to be 180-2x.

 

[Smile12345]

Sorry, unfortunately I can't see your pic... Is it possible to put it into another program?

Sorry, I hope you haven't taken that Triangle ABC is a right angle... My diagram isn't quite right... My bad fault... Please forgive me.

 

[Smile12345]

It's more like this but the smaller two triangles are congruent...

 

[Carrotsticks]

Sorry, unfortunately I can't see your pic... Is it possible to put it into another program?

Sorry, I hope you haven't taken that Triangle ABC is a right angle... My diagram isn't quite right... My bad fault... Please forgive me.

I didn't assume it was right angled.

 

[Smile12345]

I didn't assume it was right angled.

View attachment 28364

That's good... Thanks heaps... Got your pic now...

 

[Drongoski]

Q6: My version


Since XBZY is a //gram: XY//BC and AB//YZ

ZY = XB (.: = AX) [opp sides of //gram]

< AXY = < ABC = @ say [corresp <'s, XY//BZ]

< YZC = < ABC = @ [corresp <'s, AB//YZ]

< AYX = < YCZ = & say [corresp <'s, XY//BC]

.: in triangles AXY and YZC:

- < AYX = < YZC [=@]

- < AYX = < YCZ [=&]

- AX = YZ

.: triangles AXY and YZC are congruent [AAS]

.: their corresponding sides are equal

.: XY = ZC [= ZY]

.: XY = XB [since ZY = XB]

.: //gram XBZY is a rhombus [since its 4 sides are equal]

 

[Smile12345]

Q6: My version


Since XBZY is a //gram: XY//BC and AB//YZ

ZY = XB (.: = AX) [opp sides of //gram]

< AXY = < ABC = @ say [corresp <'s, XY//BZ]

<YZC = < ABC = @ [corresp <'s, AB//YZ]

<AYX = < YCZ = & say [corresp <'s, XY//BC]

.: in triangles AXY and YZC:

- <AYX = < YZC [=@]

- < AYX = < YCZ [=&]

- AX = YZ

.: triangles AXY and YZC are congruent [AAS]

.: their corresponding sides are equal

.: XY = ZC [= ZY]

.: XY = XB [since ZY = XB]

.: //gram XBZY is a rhombus [since its 4 sides are equal]

Thanks heaps...