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How do you prove triangles are congruent if you only have expressions for side and angle measures?
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.
What else can I help you with?
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 have equivalent angle measures then they are congruent?
If two triangles have equivalent angle measures, they are similar, but not necessarily congruent. Similar triangles have the same shape but can differ in size, meaning their corresponding sides are proportional, but not necessarily equal. Congruent triangles must have both equal angles and equal side lengths. Therefore, while equivalent angles imply similarity, they do not guarantee congruence.
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.
Are angles congruent when their side measures are the same?
Yes, angles are congruent when their side measures are the same, specifically in the case of triangles. If two angles have sides of equal length, they can be considered congruent due to the properties of isosceles triangles or by using the Side-Angle-Side (SAS) or Angle-Side-Angle (ASA) congruence criteria. However, for angles outside of triangles, having the same side lengths does not guarantee congruence unless the angles are formed in a context where their measures can be directly compared.
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 have equivalent angle measures then they are congruent?
If two triangles have equivalent angle measures, they are similar, but not necessarily congruent. Similar triangles have the same shape but can differ in size, meaning their corresponding sides are proportional, but not necessarily equal. Congruent triangles must have both equal angles and equal side lengths. Therefore, while equivalent angles imply similarity, they do not guarantee congruence.
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.
Are angles congruent when their side measures are the same?
Yes, angles are congruent when their side measures are the same, specifically in the case of triangles. If two angles have sides of equal length, they can be considered congruent due to the properties of isosceles triangles or by using the Side-Angle-Side (SAS) or Angle-Side-Angle (ASA) congruence criteria. However, for angles outside of triangles, having the same side lengths does not guarantee congruence unless the angles are formed in a context where their measures can be directly compared.
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.
The triangles shown below may not be congruent.?
To determine if the triangles are congruent, we need to compare their corresponding sides and angles. Congruence between triangles can be established using criteria such as Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), and Angle-Angle-Side (AAS). If the triangles do not meet any of these criteria, they are not congruent. Thus, without specific measurements or angles, we cannot conclude that the triangles are congruent.
