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How do you prove triangles are congruent if you only have expressions for side and angle measures?
Wiki User
∙ 12y ago
How many sides of each triangle and how many angles of each triangle do you have ?
If you have two sides and the angle between them, or two angles and the side
between them, equal to the same parts of the other triangle, then your triangles
are congruent.
You don't even have to know what the actual numbers are. If the expressions
are equal, then the sides or angles are equal.
Wiki User
∙ 12y ago
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If two triangles have a congruent angle and two congruent sides then are the triangles guaranteed to be congruent?
Only if the congruent angle is the angle between the two congruent sides (SAS postulate).
If two triangles are similar are they congruent?
no: if you have two triangles with the same angle measurements, but one has side lengths of 3in, 4in, and 5in and the other has side lengths of 6in, 8in, and 10in, then they are similar. Congruent triangles have the same angle measures AND side lengths.
Can you show that two triangles are congruent by angle-angle-angle?
No, because they need not be congruent.
What does angle angle side mean?
Angle Angle Side is a method one can use to prove that two triangles are congruent. Basically, if any two pairs of angles and the side between these angles are congruent, then the triangles are congruent as well.
Can two triangles be congruent if all three angles have exactly the same measures?
No, they cannot, because if you think about it, the sides can be different proportional lengths but have the same angle measures.
If an angle bisector of an isosceles triangle yields two isosceles triangles what were the angle measures of the original triangle?
they would be congruent triangles!
If two triangles have a congruent angle and two congruent sides then are the triangles guaranteed to be congruent?
Only if the congruent angle is the angle between the two congruent sides (SAS postulate).
If two triangles are similar are they congruent?
no: if you have two triangles with the same angle measurements, but one has side lengths of 3in, 4in, and 5in and the other has side lengths of 6in, 8in, and 10in, then they are similar. Congruent triangles have the same angle measures AND side lengths.
Can you show that two triangles are congruent by angle-angle-angle?
No, because they need not be congruent.
Can two scalene triangles not be congruent but have 5 congruent parts?
No. Any three consecutive congruent parts (angle-side-angle or side-angle-side) make any two triangles completely congruent.
In two triangles have a congruent angle and two congruent angle and two congruent sides then the triangles are guaranteed to be congruent?
Yes, if two triangles have two congruent angles and two congruent sides then the triangles are guaranteed to be congruent. They only need two angles and one side congruent or two sides and one angle in order to be congruent.
If any two sides and any angle are congruent in two triangles then the triangles must be congruent?
False
Why is there not an angle angle angle theroem?
Because angle angle angle does not necessarily give rise to congruent triangles - they can be similar, but non-congruent.
What does angle angle side mean?
Angle Angle Side is a method one can use to prove that two triangles are congruent. Basically, if any two pairs of angles and the side between these angles are congruent, then the triangles are congruent as well.
Can two triangles be congruent if all three angles have exactly the same measures?
No, they cannot, because if you think about it, the sides can be different proportional lengths but have the same angle measures.
What are right triangle congruence theorem?
1.HyL Theorem (Hypotenuse-Leg) - if the hypotenuse and leg of one triangle is congruent to another triangle's hypotenuse and leg, then the triangles are congruent. 2.HyA (Hypotenuse-Angle) - if the hypotenuse and angle of one triangle is congruent to another triangle's hypotenuse and angle, then the triangles are congruent. 3.LL (Leg-Leg) if the 2 legs of one triangle is congruent to another triangle's 2 legs, then the triangles are congruent. 4.LA (Leg-Angle) if the angle and leg of one triangle is congruent to another triangle's angle and leg, then the triangles are congruent.
Are two scalene triangles with congruent angles similar?
When all of their corresponding angles are congruent (in any triangle, in fact) then the triangles are similar. Similarity postulate AAA. (angle-angle-angle)
