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Only if the two triangles are congruent will they have equal areas.
A third fact is required to determine they are congruent (and thus have the same area):
1) The third sides are equal;
2) The angles enclosed between the sides are equal; or
3) The same one of the sides is the hypotenuse of the triangles, which are right angled triangles.
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What condition for a triangle produce triangles that have the same area?
If another triangle has the same three sides, that is, sides of the same length, it will have the same area. Note that this is a sufficient, but not a necessary, condition, since you can also have triangles of a different shape that have the same area.
Does an isosceles triangle have two sides of equal length?
The definition of an isosceles triangle is a triangle with at least two sides of equal length, which means it also has two angles of equal measurement. As such, equilateral triangles; triangles in which all sides and angles are congruent (Of the same size) are also considered to be isosceles triangles.
If two triangles are congruent?
Then they both will be identical in sides and angles
How are equilateral isosceles and scalene different?
And Equilateral Triangle has three EQUAL sides. Basically just your ordinary triangle. The Isosceles triangle usually has TWO equal sides, and one odd side,( not the same size in degrees.) A scalene Triangle also has TWO of the same sides, BUT- Its degrees are usually always different. I'll show you some examples. The first example below is an isosceles Triangle. The 2nd is the Scalene Triangle... Hope I helped...
What is the different between all of the 4 triangles?
Equilateral triangles have 3 sides all of the same lengths and the three angles are equal (60°). Isoceles triangles have two sides of equal length with both of those side angles being equal while the other is different. Scalane triangles have all sides of different lengths and different angles. Right angled triangles have one angle of 90° and the other two will total 90°.
Triangles are congruent if they have the same what?
Triangles are congruent if they have the same size and shape, meaning their corresponding sides and angles are equal.
Why are scalene triangles and equilateral triangles the same?
They are not the same. An equilateral triangle has 3 equal sides, while a scalene triangle has no equal sides.
How you can prove that the angles of two triangles are equal?
If the angles of two triangles are equal the triangles are similar. AAA If you have three angles on both triangles these must be equal for the triangles to be similar. SAS If you have an angle between two sides and the length of the sides and the angle are the same on both triangles, then the triangles are similar. And SSS If you know the three sides
What condition for a triangle produce triangles that have the same area?
If another triangle has the same three sides, that is, sides of the same length, it will have the same area. Note that this is a sufficient, but not a necessary, condition, since you can also have triangles of a different shape that have the same area.
What are iscosoles and scalene triangles?
iscosoles triangles have two angles that are equal with two of the same lenght sides and scalene triangle have no sides or angles that are the same
What do triangles need to have to be congruent?
the same shape compared to another with equal sides
Does an Isosceles have two equal sides?
Yes. Isosceles triangles have two identical sides and angles. They are also longer than the third side.All triangles have three sides. Isosceles triangles have two sides of the same length.
Are Equilateral and equivalent triangles the same thing?
No Equilateral triangles are triangles that have all of its three sides the same exact measurement. This means that if all the sides are the same then all of the interior angles will equal the same. And they always equal 60 degrees in an equilateral triangle. Equivalent traingles are just traingles that are equal in size and angles to another triangle equal. Equivalent traingles can be equilateral but they do not have to be.
Does an isosceles triangle have two sides of equal length?
The definition of an isosceles triangle is a triangle with at least two sides of equal length, which means it also has two angles of equal measurement. As such, equilateral triangles; triangles in which all sides and angles are congruent (Of the same size) are also considered to be isosceles triangles.
If two triangles are congruent?
Then they both will be identical in sides and angles
Will the lengths of two corresponding altitudes of similar triangles will have the same ratio as any pair of corresponding sides?
It is given that two triangles are similar. So that the ratio of their corresponding sides are equal. If you draw altitudes from the same vertex to both triangles, then they would divide the original triangles into two triangles which are similar to the originals and to each other. So the altitudes, as sides of the similar triangles, will have the same ratio as any pair of corresponding sides of the original triangles.
Can any two triangles be joined to make a rhombus?
No. A rhombus has all four sides of equal length. To split a rhombus into only 2 triangles, it must be split along a diagonal; which means that 2 of the sides of one of the triangles must be the same length as the sides of the rhombus, which being equal mean the triangles must be (at least) isosceles - scalene triangles will not work. Further, as the diagonal will be a common length to each of the triangles (the length of their third sides), it will form the base (ie the side opposite the vertex between the sides of equal length) of the isosceles triangles, and so the triangles must be to congruent isosceles triangles. If the diagonal has the same length as the side of the rhombus, then the two congruent triangles will be congruent equilateral triangles.
