source : splashlearn.com
What is Obtuse Triangle? – [Definition, Facts & Example]
What is Obtuse Triangle?
An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees. In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°.
Here, the triangle ABC is an obtuse triangle, as ∠A measures more than 90 degrees. Since, ∠A is 120 degrees, the sum of ∠B and ∠C will be less than 90° degrees.
In the above triangle, ∠A + ∠B + ∠C = 180° (because of the Angle Sum Property)
Since ∠A = 120°, therefore, ∠B + ∠C= 60°.
Hence, if one angle of the triangle is obtuse, then the other two angles with always be acute.
Some examples of obtuse triangles:
Non-examples of obtuse triangles:
Special facts about obtuse triangle:
An equilateral triangle can never be obtuse. Since an equilateral triangle has equal sides and angles, each angle measures 60°, which is acute. Therefore, an equilateral angle can never be obtuse-angled.
A triangle cannot be right-angled and obtuse angled at the same time. Since a right-angled triangle has one right angle, the other two angles are acute. Therefore, an obtuse-angled triangle can never have a right angle; and vice versa.
The side opposite the obtuse angle in the triangle is the longest.
Obtuse angled triangles in real life:
In our surroundings, we can find many examples of obtuse triangles. Here are some examples:
OneClass: Triangle ABC is an obtuse triangle with the – Triangle ABC is an obtuse triangle with the obtuse angle at vertex B, then angle A must be equal to _____?By the Alternate Interior Angle Theorem , ∠ 2 ≅ ∠ 3 . Therefore, by transitive property, ∠ 4 ≅ ∠ 3 . Since the angles ∠ 3 and ∠ 4 are congruent , the triangle Δ A B E is an isosceles triangle with A E = A B .Which of the following angle measures can form an obtuse triangle ABC? a) 60°, 70°,50° b) 95°, 30°, 55° c) 89°,45°,46° d) 90°, 60°, 30° Solution: An obtuse triangle has one of the vertex angles as an obtuse angle (> 90 °). Among the given options, option (b) satisfies the condition.
Triangle Angle Bisector Theorem – Varsity Tutors – We have to find the correct statement for angle A in a triangle ABC, which is an obtuse triangle. We know that angle B is obtuse (greater than 90 degrees). Therefore angles A and C must be less than 90 degrees. Angle A can not be congruent to angle B (angle B > angle A).Triangle ABC is an obtuse triangle with the obtuse angle at vertex B. Angle A must be less than 90°. greater than 90°. congruent to angle B. congruent to angle C.if the measures of the angles of a triangle are represented by 2x, 3x-15, and 7x-15, the triangle is 1)an isosceles triangle 2)a right triangle 3)an acute triangle 4)an equiangular triangle . Math. To describe a sequence of transformations that maps triangle ABC onto triangle A''B''C'', a student starts with a reflection over the x-axis.
Obtuse Angled Triangle | Formula and Properties | Solved – Question: Triangle ABC is an obtuse triangle with the obtuse angle at the vertex B angle A must be? Answers Mine. US. Ask your question Login with google. Search. adminstaff. 19/01/2020 07:31 AM. Mathematics. 1 Answers.Triangle ABC is an obtuse triangle with the obtuse angle at vertex B. Angle A must be less than 90°. greater than 90°. congruent to angle B.Triangle ABC is an obtuse triangle with the obtuse angle at vertex B. Angle A must be 2 See answers 9oradford 9oradford it will be a acute angle. inkaraven inkaraven angle A have to be less than 90 degrees.. the obtuse angle is more than 90 degrees. Angle C is less than 90 degrees. New questions in Math.