Isosceles Triangle Practice Problems with Solutions

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.

To solve this problem, we need to analyze the given side lengths of the triangle and determine its type based on these lengths.

The side lengths provided are 8, 8, and 8.

According to the definitions of triangle types:

• An equilateral triangle has all sides equal.
• An isosceles triangle has at least two sides equal.
• A scalene triangle has all sides different.

In this case, since all three side lengths are equal (8 = 8 = 8), the triangle is not a scalene triangle, because a scalene triangle requires all three sides to have different lengths.

Therefore, the triangle with sides 8, 8, and 8 is not a scalene triangle. The answer is No.

An acute-angled triangle is defined as a triangle where all three interior angles are less than $90^\circ$.

In examining the visual depiction of the triangle provided in the problem, we need to see if it appears to satisfy this property. The assessment relies on observing the triangle's structure shown in the drawing and noting any geometric indications suggesting angle types.

Given the information from the drawing, if all angles seem to satisfy the condition of being less than $90^\circ$, then by definition, the triangle is an acute-angled triangle.

Conclusively, the answer to whether the triangle is acute-angled based on provided visual assessment and inherent assumptions in its illustration is: Yes.

To ascertain whether the triangle in the drawing is acute, we need to examine the orientation and notation within the visual representation. The drawing vividly illustrates a triangle featuring a small square at one of the angles, a universal sign indicating a right angle. A right angle measures $90^\circ$, rendering it impossible for the triangle to be classified as acute since an acute triangle requires all angles to be less than $90^\circ$.

Therefore, given the right angle in the drawing, the triangle cannot be an acute-angled triangle. Consequently, the correct choice is:

No (:

No

To determine if the triangle in the diagram is isosceles, we will follow these steps:

• Step 1: Identify key components of the triangle.
• Step 2: Calculate the lengths of the triangle’s sides.
• Step 3: Compare the side lengths to see if any two are equal.

From the diagram, notice the triangle appears to be a right triangle:

• We assume the base is along the horizontal from point $A$ (the right angle at (239.132, 166.627)) to point $B$ (another corner at (1091.256, 166.627)).
• The height runs vertically from point $A$ upwards (perpendicular to base).
• Hypotenuse is the line from $B$ to the topmost point (apex) of the triangle.

Let's calculate the distances:

The calculations above fail specific resolution. Evaluating actual differences on H-plane with conceptual shows all side lengths differ, as:

• Base $AB$ is longer than a side, potentially unmatched without midpoint coordinates or visually explained data specifically given line ratios.
• Existing $AC$ equal hypothesized renders Pythagorean unresolved exceeding functional equality proof due diagram inadequacy.

Therefore, since no direct component proves equivalence, the solution yields:

No, the triangle is not isosceles.