# Triangle-related Questions

• Jan 20th 2008, 06:09 AM
~NeonFire372~
Triangle-related Questions
I have a few questions that I don't completely understand and those are:

1. What does congruence mean for triangles? [I didn't think it "meant" anything for triangles other than the fact that they are congruent]

2. Do two congruent triangles have the same area?

3. Are all triangles with the same area congruent?

I find all this confusing even though it's pretty basic.
• Jan 20th 2008, 06:14 AM
earboth
Quote:

Originally Posted by ~NeonFire372~
I have a few questions that I don't completely understand and those are:

1. What does congruence mean for triangles? [I didn't think it "meant" anything for triangles other than the fact that they are congruent]

2. Do two congruent triangles have the same area?

3. Are all triangles with the same area congruent?

I find all this confusing even though it's pretty basic.

Hello,

#1: Two triangles are congruent if their corresponding sides and angles are equal.

#2: Yes

#3: No
• Jan 20th 2008, 06:16 AM
~NeonFire372~
Could you explain why for number 2 and 3 a bit more?
• Jan 20th 2008, 06:21 AM
earboth
Quote:

Originally Posted by ~NeonFire372~
Could you explain why for number 2 and 3 a bit more?

I've attached a drawing of a lot of triangles which have the same area (btw. why?) but they are not congruent because they differ in the length of corresponding sides and the value of corresponding angles.

EDIT: Have a look here: Congruent Triangles
• Jan 20th 2008, 06:25 AM
~NeonFire372~
So...

Triangles with the same area are "not congruent because they differ in the length of corresponding sides and the value of corresponding angles" and triangles that are congruent always have the same area because the sides and angles are the same?
• Jan 20th 2008, 06:27 AM
earboth
Quote:

Originally Posted by ~NeonFire372~
So...

Triangles with the same area are "not necessarily congruent because they differ in the length of corresponding sides and the value of corresponding angles" and triangles that are congruent always have the same area because the sides and angles are the same?

Correct! (Clapping)
• Jan 20th 2008, 06:29 AM
~NeonFire372~
Thanks. (Whew)