Possible response: Condition 6 does not determine a unique triangle because the condition of two sides and an acute non-included angle determines two possible triangles when the side adjacent to the angle is longer than the side opposite the angle.
What does not determine a unique triangle?
A triangle drawn under the condition of two sides and a non-included angle, where the angle is acute, does not determine a unique triangle. … A triangle drawn under the condition of two sides and a non-included angle, where the angle is 90° or greater, does determine a unique triangle.
Is AAA a unique triangle?
Knowing only angle-angle-angle (AAA) does not work because it can produce similar but not congruent triangles. … Because there are 6 corresponding parts 3 angles and 3 sides, you don’t need to know all of them.
Which theorem does determine a unique triangle?
corresponding sides are equal under some correspondence; two angle measurements and a given side length of a triangle determine a unique triangle. two angles and included side condition and (2) the two angles and the side opposite a given angle condition.
Is SSA a unique triangle?
Given triangular parts SSS, ASA or AAS always guarantees a single, unique triangle. Given the triangular parts SSA, however, is different and leaves the triangle unclear, or ambiguous. … Hence, there are no possible triangles and nothing to solve for.
How many unique triangles can make?
With this information, one unique triangle can be made. Sometimes, two or more different triangles can be made with three given measures. For example, here are two different triangles that can be made with an angle measuring and side lengths 6 and 8. Notice the angle is not between the given sides. You may also read,
Is there an AAA Theorem?
may be reformulated as the AAA (angle-angle-angle) similarity theorem: two triangles have their corresponding angles equal if and only if their corresponding sides are proportional. Check the answer of
What does a unique triangle look like?
A unique triangle will be produced if you are given: all three sides (Side-Side-Side) two sides and the included angle (Side-Angle-Side) two angles and the included side (Angle-Side-Angle)
What does a unique triangle mean?
A unique triangle means there is ONLY ONE WAY to create the triangle. All unique triangles are congruent (the same) even though you may have to “flip” or “turn” them to line up. Criteria For A Unique Triangle. Read:
Does a triangle with side lengths of 15 12 and 9 exist?
Therefore yes, it is a right triangle.
What are the 5 triangle congruence theorems?
There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL.
Why is there no SSA postulate?
What about SSA (Side Side Angle) theorem? … The ASS Postulate does not exist because an angle and two sides does not guarantee that two triangles are congruent. If two triangles have two congruent sides and a congruent non included angle, then triangles are NOT NECESSARILLY congruent.
How do you tell if there are two triangles?
Once you find the value of your angle, subtract it from 180° to find the possible second angle. Add the new angle to the original angle. If their sum is less than 180°, you have two valid answers. If the sum is over 180°, then the second angle is not valid.
Can you make 2 different triangles with the same 3 side lengths?
Side-side-side (SSS) is one of those congruence theorems in geometry class that proves if two triangles have the same side lengths, they are congruent triangles. Therefore, there can only be one unique triangle formed by a set of three line segments. … So if it is possible to form the triangle, there can be only one.
How many different triangles are there?
To learn about and construct the seven types of triangles that exist in the world: equilateral, right isosceles, obtuse isosceles, acute isosceles, right scalene, obtuse scalene, and acute scalene. Geometry Sticks.
