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How can you say that if areas of two triangles are equal then they are congruent?
In order for a triangle to be congruent the two triangles have to be the same shape and size, thus they are congruent if they can be moved into an isometry or any other combination. But you're asking how a question which has two possibilities. Assuming that you have two triangles whose sides are equivalent which makes the areas equal to each other then you can state the side-side-side rule which is if the three sides of one triangle is equivalent to the other three sides of the other triangle then they are congruent. But if you have an angle present in the triangles you could argue the angle angle side rule, but if the angles are joint you would argue the angle side angle. But if one triangle has one degree and the other one has a different degree then they will not be congruent.
It appears from the name of the HL Theorem that you actually need to know that only two parts of two triangles are congruent in order to prove two triangles congruent Is this the case?
No. You can know all three angles of both and all you can say is that the triangles are similar. Or with any pair of congruent sides you can have an acute angle between them or an obtuse angle.
How do you prove the hinge theorem?
If of triangle ABC and A'B'C' sides AB = A'B' and AC = A'C', and the included angle at A is larger than the included angle at A*, then BC > B'C'.Proof:A A'/|\ /|/ | \ / |/ | \ / |/ | \ B'/ |B | X \C |C'DWe construct AD such that AD = A'C' = AC and angle BAD = angle B'A'C'.Triangles ABD and A'B'C' are congruent. Therefore BD = B'C'.Let X be the point where the angle bisector of angle DAC meets BC.From the congruent triangles AXC and AXD (SAS) we have that XD = XC.Now, by the triangle inequality we have that BX + XD > BD, so BX + XC > BD, and consequently BC > BD = B'C'.
What is the AAA theorem and the SSS postulate?
There is no AAA theorem since it is not true. SSS is, in fact a theorem, not a postulate. It states that if the three sides of one triangle are equal in magnitude to the corresponding three sides of another triangle, then the two triangles are congruent.
If a quad has 4 congruent sides but its diagonals are not congruent then what is the quad?
non square rhombus
What do the triangles look like and what are the names?
Equilateral triangle = All sides congruent Scalene triangle = No sides congruent Isosceles triangle = At LEAST two sides congruent Right triangle = Triangle with one right angle Obtuse triangle = Triangle with ONE obtuse angle Acute triangle = Triangle with ALL acute angles
What triangle has an obtuse angle and no congruent sides?
A scalene triangle can have an obtuse angle and two different acute angles.
Classification of triangle?
Classification of triangles according to sides: -Scalene Triangle - a triangle with no 2 congruent sides. -Isosceles Triangle - a triangle with at least 2 congruent sides. -Equilateral Triangle - a triangle with 3 congruent sides. Classification of triangles according to angles: -acute triangle - a triangle with 3 acute angles. -right triangle - a triangle with one right angle. -equiangular triangle - a triangle with 3 congruent angles. -obtuse triangle - a triangle with one obtuse angle.
An acute triangle has only two congruent sides?
An acute triangle may have three, two, or no congruent sides.
How do you name a triangle by its sides and angles?
how you name a triangle by its angles is like acute, obtuse, or right triangle. you do that by seeing if the angle has a 90 degree angle in it then its a right angle, if all the angles are 90 degrees or less than its an acute triangle. and if the triangle has one angle that is over 90 degrees than it is an obtuse triangle. to name a triangle by its sides is if its equilateral, equiangular, or regular. if its equilateral then all the sides are congruent. if its equiangular then all the angles are congruent. if its regular, then all the sides and angles are congruent to each other (for example and octogon). :)
A triangle with 3 congruent sides?
acute triangle
What is triangle is an obtuse triangle?
An obtuse triangle is a type of triangle that has no congruent sides. Basically none of its sides are the same size.
Does an acute triangle have two congruent sides?
Not every acute triangle has two congruent sides, although some do, in which case they are called isosceles triangles.
What figure shows a triangle with no sides congruent and 1 obtuse angle?
An obtuse triangle whose other two angles will be acute angles
What type of triangle has 1 right angle and 2 congruent sides?
Isosceles Triangle - 2 congruent sides Equilateral Triangle - all three sides are congruent Scalene triangle - no sides are congruent
What are the names of the triangles and how can you tell?
right triangle forms a 90 degree angle scalene triangle has no congruent sides isosceles triangle has at least 2 congruent sides equilateral triangle has 3 congruent sides acute triangle all angles measure less than 90 degrees and the obtuse triangle contains 1 obtuse angles.
What is Side Angle Side?
If two sides and the included angle of one of one of the triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
