Isosceles Triangle Practice Problems with Solutions

Remember that the sum of angles in a triangle is equal to 180.

In an equilateral triangle, all sides and all angles are equal to each other.

Therefore, we will calculate as follows:

$x+x+x=180$

$3x=180$

We divide both sides by 3:

$x=60$

To solve this problem, we'll follow these steps:

• Step 1: Identify the properties of a right triangle.
• Step 2: Identify the properties of an equilateral triangle.
• Step 3: Compare these properties to determine if a right triangle can be equilateral.

Now, let's work through each step:

Step 1: A right triangle is defined by having one angle equal to $90^\circ$.
Step 2: An equilateral triangle is defined by having all three sides of equal length and all three angles equal to $60^\circ$.
Step 3: Compare the angle measurements: A right triangle cannot have all angles $60^\circ$ because it requires one angle to be $90^\circ$. Likewise, an equilateral triangle cannot have a $90^\circ$ angle, as all its angles must be $60^\circ$.

Therefore, it is impossible for a right triangle to be equilateral, as they fundamentally differ in angle requirements.

The answer to the problem is No.

Let's note in which of the triangles angle B forms a right angle, meaning an angle of 90 degrees.

In answers C+D, we can see that angle B is smaller than 90 degrees.

In answer A, it is equal to 90 degrees.

Let's analyze the problem to understand how the angles are defined in a right triangle.

A right triangle is defined as a triangle that has one angle equal to $90^\circ$. This is known as a right angle. Because the sum of all angles in any triangle must be $180^\circ$, the two remaining angles must add up to $90^\circ$ (i.e., $180^\circ - 90^\circ$).

In a right triangle, the right angle is always present, leaving the other two angles to be less than $90^\circ$ each. These angles are called acute angles. An acute angle is an angle that is less than $90^\circ$.

To summarize, the angle types in a right triangle are:

• One angle that is $90^\circ$ (a right angle).
• Two angles that are each less than $90^\circ$ (acute angles).

Given the choices, the description "Straight, sharp" correlates to the angle types in a right triangle, as "Straight" can be associated with the $90^\circ$ angle (though it's generally called a right angle) and "Sharp" correlates with acute angles.

Therefore, the correct aspect of the other two angles in a right triangle are straight (right) and sharp (acute), which matches the correct choice.

Therefore, the solution to the problem is Straight, sharp.

To determine if the triangle in the diagram is obtuse, we will visually assess the angles:

• Step 1: Identify the angles in the diagram. The triangle has three angles, with one angle appearing between the horizontal base and the left slanted side.
• Step 2: Evaluate the angle between the base and the left side. If it opens wider than a right angle, it's considered obtuse. This angle seems to be greater than $90^\circ$, indicating obtuseness.
• Step 3: Conclude based on visual inspection. Since this key angle is greater than $90^\circ$, the triangle must be an obtuse triangle.

Therefore, the solution to the problem is Yes; the diagram does show an obtuse triangle.