An obtuse triangle is a triangle that has one obtuse angle (greater than degrees and less than degrees) and two acute angles (each of which is less than degrees). The sum of all three angles together is degrees.
An obtuse triangle is a triangle that has one obtuse angle (greater than degrees and less than degrees) and two acute angles (each of which is less than degrees). The sum of all three angles together is degrees.
In a right triangle, the side opposite the right angle is called....?
Next, we will look at some examples of obtuse triangles:
Homework:
Calculate which is larger
Given that the triangle is an obtuse triangle.
Which angle is larger or ?
Solution:
Since we are given that the triangle is an obtuse triangle, we understand that is not greater than .
In a triangle, there is only one obtuse angle therefore the answer is:
Answer:
In an isosceles triangle, what are each of the two equal sides called ?
In a right triangle, the two sides that form a right angle are called...?
Is the triangle in the drawing a right triangle?
Given the triangle .
is obtuse.
The sum of the acute angles in the triangle is equal to .
Find the value of angle .
Solution:
Since we know that is obtuse, we are certain that angles and are acute.
This means that we have the information that the sum of the acute angles
The sum of the angles in a triangle is equal to .
Answer:
Given the obtuse triangle .
,
Task:
Is it possible to calculate ?
If so, calculate it.
Solution:
Given that:
We substitute:
Answer: yes, .
Is the triangle in the drawing a right triangle?
Fill in the blanks:
In an isosceles triangle, the angle between two ___ is called the "___ angle".
Is the triangle in the drawing a right triangle?
Assignment
Which triangle is given in the drawing?
Solution
Since angles and : are both equal to , we know that the opposite sides are also equal, therefore the triangle is isosceles.
Answer
Isosceles triangle
Assignment
Determine which of the following triangles is obtuse, which is acute, and which is right:
Solution
Let's observe triangle and check if it satisfies the Pythagorean theorem, therefore we replace the data we have:
We solve the equation
The sum of the squares of the "perpendicular" is greater than the square of the rest, therefore the triangle is an isosceles triangle.
Let's observe triangle and check if it satisfies the Pythagorean theorem, therefore we replace the data we have:
We solve the equation
The sum of the squares of the "perpendicular" is less than the square of the other, therefore the triangle is obtuse
Let's observe triangle and check if the Pythagorean theorem is satisfied, first we calculate what is the square root of
This is the largest side among the: and we will refer to it as "hypotenuse".
Now we replace the data we have:
We solve the equation
In this triangle, the Pythagorean theorem is satisfied and therefore the triangle is right.
Answer
A: acute angle B: obtuse angle C: right angle
In an isosceles triangle, the third side is called?
In an isosceles triangle, the angle between ? and ? is the "base angle".
Choose the appropriate triangle according to the following:
Angle B equals 90 degrees.
What kind of triangle is given in the drawing?
As all the angles of a triangle are less than 90° and the sum of the angles of a triangle equals 180°:
The triangle is isosceles.
Isosceles triangle
Given the values of the sides of a triangle, is it a triangle with different sides?
As is known, a scalene triangle is a triangle in which each side has a different length.
According to the given information, this is indeed a triangle where each side has a different length.
Yes
Which kind of triangle is given in the drawing?
As we know that sides AB, BC, and CA are all equal to 6,
All are equal to each other and, therefore, the triangle is equilateral.
Equilateral triangle
Is the triangle in the drawing a right triangle?
Due to the presence of the 90 degree angle symbol we can determine that this is indeed a right-angled triangle.
Yes
What kid of triangle is the following
Given that in an obtuse triangle it is enough for one of the angles to be greater than 90°, and in the given triangle we have an angle C greater than 90°,
Furthermore, the sum of the angles of the given triangle is 180 degrees so it is indeed a triangle:
The triangle is obtuse.
Obtuse Triangle