Congruent triangles

[blu3fan]

Can anyone please help me and give me the rules for the congruence of two triangles ?

[keentoknow]

Two triangles ABC and MNP are congruent if:

1. AB=MN;AC=MP and angle CAB= angle PMN (called SAS rule)

2. angle CAB= angle PMN; angle CBA = angle PMN and AB=MN (ASA rule)

3. AB=MN; AC=MP; BC=NP (SSS rule)

4. AB=MN; AC=MP angle ACB= angle MNP and AB >AC.

A problem for you: Show that ABC is congruent to MNP if AB=MN and the medians AA1=MM1; BB1=NN1;

[dancho]

A problem for you: Show that ABC is congruent to MNP if AB=MN and the medians AA1=MM1; BB1=NN1

How can we prove that ABC is congruent to MNP
following the up rules?

[keentoknow]

Hint: Medians intersect at a point G. What properties G has?

[dancho]

It reminds me that if G1 and G2 are the intersept points of the medians
then ABG1 and MNG2 are congruent, because of the properties of medicenters.

Then ?

[keentoknow]

What about BG1A1 and NG2A2?

[dancho]

I see now.
They are congruent too.
So angle B = angle M

The same way we prove that:
angle B = angle M

And by angle-side-angle the two triangles are congruent

You are quite cleaver to think of such an interesting problem!

[keentoknow]

If You liked this one here are 2 more:

1. Show that ABC is congruent to MNP if AB=MN and the medians AA1=MM1; CC1=PP1.

2. Show that ABC is congruent to MNP if AB=MN, AC=MP and the median AA1=MM1.

2 is a hard one.

Where are u from, what is your age?

[dancho]

I am 15 years old(8 grade) from Bulgaria.
What about you ?

[Guest]

I think that two triangles ABC and DEF are congruent when every corresponding side has the same length, and every corresponding angle has the same measure means the side AB's length should be equal to DE and same with the angle the angle at A has the same measure as the angle at D, I hope this can help you.

[leesajohnson]

1) AB=MN;AC=MP and angle CAB= angle PMN

2) Angle CAB= angle PMN; angle CBA = angle PMN and AB=MN