# How do you know if a triangle is 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.

Types of Triangle For example, a scalene triangle (no sides the same length) can have one interior angle 90°, making it also a right triangle. This would be called a “right scalene triangle“.

Furthermore, what is a unique polygon? The Unique Polygon Theorem is: All regular polygons with the same number of sides are similar.

Subsequently, question is, what creates a unique triangle?

The two angles and any side condition determines a unique triangle. Since the condition has two different arrangements, we separate it into two conditions: the two angles and included side condition and the two angles and the side opposite a given angle condition.

What is a more than one triangle?

In general, a unique triangle may always be drawn if three side lengths are given and the sum of any two is greater than the third. c) More than one triangle can be drawn with Angle A = 40°, Angle B = 60° and Angle C = 80°. When two sides and an included angle are defined, then a unique triangle may always be drawn.

### What are unique triangles?

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.

### Is AAA a unique triangle?

Knowing only angle-angle-angle (AAA) does not work because it can produce similar but not congruent triangles. When you’re trying to determine if two triangles are congruent, there are 4 shortcuts that will work. Because there are 6 corresponding parts 3 angles and 3 sides, you don’t need to know all of them.

### How many unique triangles can make?

Answer: 15 unique triangles can be made. Step-by-step explanation: Given : A triangle has one angle measures 60° and another angle is an obtuse angle .

### What makes a triangle not a triangle?

The Formula. The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side. In other words, as soon as you know that the sum of 2 sides is less than (or equal to) the measure of a third side, then you know that the sides do not make up a triangle.

### Is an equilateral triangle unique?

An equilateral triangle is one in which all three sides are congruent (same length). Because it also has the property that all three interior angles are equal, it really the same thing as an equiangular triangle. See Equiangular triangles.

### How do you determine if the ambiguous case is given?

When you are given two sides and an angle not in between those sides, you need to be on the lookout for the ambiguous case. To determine if there is a 2nd valid angle: 1. See if you are given two sides and the angle not in between (SSA).

### How do you know if it’s ambiguous case?

If angle A is acute, and a = h, one possible triangle exists. If angle A is acute, and a > b, one possible triangle exists. If angle A is acute, and h < a < b, two possible triangles exist. If angle A is obtuse, and a < b or a = b, no such triangle exists.

### What is an ambiguous triangle?

For those of you who need a reminder, the ambiguous case occurs when one uses the law of sines to determine missing measures of a triangle when given two sides and an angle opposite one of those angles (SSA). If angle A is acute, and a = h, one possible triangle exists.

### What is ambiguous cases of a triangle?

The “Ambiguous Case” (SSA) occurs when we are given two sides and the angle opposite one of these given sides. The triangles resulting from this condition needs to be explored much more closely than the SSS, ASA, and AAS cases, for SSA may result in one triangle, two triangles, or even no triangle at all!

### How many possible triangles are there?

There are three triangles possible {3, 4, 6}, {4, 6, 7} and {3, 6, 7}. Note that {3, 4, 7} is not a possible triangle.