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How to Prove that a triangle cannot have two right angles?
The sum of the interior angles of a triangle is 180 degrees. If one angle is 90, that leaves 90 for the other two angles. You can't have another angle of 90 and an angle of 0, so there can only be one angle in a triangle that measures 90 degrees.
Can a right triangle have two angles measure 38 and 54 degrees?
No; a right triangle cannot have two angles that are measured 38 and 54 degrees. This is because a right triangle must have one angle that is equal to 90 degrees, for this is a basic property of a right triangle. The sum of the angles in the triangle must be 180 degrees. In order to prove that there indeed cannot be a triangle with angles measuring 90, 38, and 54 degrees, you add the three. If their sum is greater than 180 degrees, then it is impossible; as in this case, where the sum totals to 182 degrees.
Can a counterexample prove that the angles of a triangle need not add up to 180 degrees?
Yes - if such a counterexample can be found. However, using only the Euclidean axioms and logical arguments, it can be proven that the angles of a triangle in a Euclidean plane must add to 180 degrees. Consequently, a counterexample within this geometry cannot exist.
Why is AAA not an appropriate conjecture for triangle congruence?
It does not necessarily prove congruence but it does prove similarity. You can have a smaller or bigger triangle that has the same interior angles.
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.
How to Prove that a triangle cannot have two right angles?
The sum of the interior angles of a triangle is 180 degrees. If one angle is 90, that leaves 90 for the other two angles. You can't have another angle of 90 and an angle of 0, so there can only be one angle in a triangle that measures 90 degrees.
Can a right triangle have two angles measure 38 and 54 degrees?
No; a right triangle cannot have two angles that are measured 38 and 54 degrees. This is because a right triangle must have one angle that is equal to 90 degrees, for this is a basic property of a right triangle. The sum of the angles in the triangle must be 180 degrees. In order to prove that there indeed cannot be a triangle with angles measuring 90, 38, and 54 degrees, you add the three. If their sum is greater than 180 degrees, then it is impossible; as in this case, where the sum totals to 182 degrees.
Can a counterexample prove that the angles of a triangle need not add up to 180 degrees?
Yes - if such a counterexample can be found. However, using only the Euclidean axioms and logical arguments, it can be proven that the angles of a triangle in a Euclidean plane must add to 180 degrees. Consequently, a counterexample within this geometry cannot exist.
Why is AAA not an appropriate conjecture for triangle congruence?
It does not necessarily prove congruence but it does prove similarity. You can have a smaller or bigger triangle that has the same interior angles.
How do you Prove that the sum of the exterior angle so formed is 360 if the sides of a triangle are produced in order?
All exterior angles of any polygon add up to 360 degrees because angles on a straight line add up to 180 degrees as for example an equilateral triangle has 3 equal interior angles of 60 degrees and so 180-60 = exteror angle of 120 degrees. Therefore 3 times 120 = 360 degrees.
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.
How can you prove that a triangle has a sum of 180?
You would add up all the angles.
How do you prove if a triangle is acute right or obtuse?
Acute is Less than 90 degrees Obtuse is more than 90 degrees Right is 90 degrees If all 3 angles are acute it's an acute triangle If 1 angle is 90 then it's Right triangle and if 1 angle is more than 90 it's obtuse triangle hoped this helped ~PinataParadise
How can proving two triangles congruent can help prove parts of the triangle congruent?
When you prove a triangle is congruent to another, it can help you prove parts of the triangle congruent by checking the ratio between all sides and angles. Thank you for asking
How do you prove that the diagonals of a square are equal and bisect each other at right angles?
it would produce two right angle triangleImproved Answer:-Measure them and use a protractor which will result in equal measures of 4 by 90 degrees angles
What is congruent angle?
Congruent angles are of the same size as for example 85 degrees is congruent to 85 degrees
What are the least number of acute angles that a triangle can have?
It must have at least 2. We can prove this by contradiction. If there is one or less acute angle, there must be two or more angles of 90 degrees or more. This adds to over 180 degrees. Since triangles can only have a total of 180 degrees, this violates the definition of a triantle, so there must be at least two acute angles.
