Isosceles Triangle Practice Problems and Exercises

Master isosceles triangles with step-by-step practice problems. Learn to identify equal sides, calculate base angles, and solve vertex angle problems.

📚Master Isosceles Triangle Properties Through Practice
  • Identify equal sides and legs in isosceles triangles
  • Calculate base angles using the equal angles property
  • Find vertex angles when given base angle measurements
  • Classify isosceles triangles as acute, right, or obtuse
  • Apply the angle sum property to solve triangle problems
  • Distinguish between base angles and vertex angles in examples

Understanding Isosceles triangle

Complete explanation with examples

Definition of isosceles triangle

The isosceles triangle is a type of triangle that has two sides (legs) of equal length.

A consequence of having two sides of equal length implies that also the two angles opposite these sides measure the same.

Detailed explanation

Practice Isosceles triangle

Test your knowledge with 20 quizzes

Given the values of the sides of a triangle, is it a triangle with different sides?

282828252525AAABBBCCC28

Examples with solutions for Isosceles triangle

Step-by-step solutions included
Exercise #1

Is the triangle in the drawing an acute-angled triangle?

Step-by-Step Solution

An acute-angled triangle is defined as a triangle where all three interior angles are less than 9090^\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 9090^\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.

Answer:

Yes

Video Solution
Exercise #2

In an isosceles triangle, the angle between ? and ? is the "base angle".

Step-by-Step Solution

An isosceles triangle is one that has at least two sides of equal length. The angles opposite these two sides are known as the "base angles."
The side that is not equal to the other two is referred to as the "base" of the triangle. Thus, the "base angles" are the angles between each of the sides that are equal in length and the base.
Therefore, when we specify the angle in terms of its location or position, it is the angle between a "side" and the "base." This leads to the conclusion that the angle between the side and the base is the "base angle."

Therefore, the correct choice is Side, base.

Answer:

Side, base.

Exercise #3

Given the values of the sides of a triangle, is it a triangle with different sides?

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Step-by-Step Solution

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.

Answer:

Yes

Video Solution
Exercise #4

Is the triangle in the drawing a right triangle?

Step-by-Step Solution

Due to the presence of the 90 degree angle symbol we can determine that this is indeed a right-angled triangle.

Answer:

Yes

Exercise #5

In an isosceles triangle, what are each of the two equal sides called ?

Step-by-Step Solution

In an isosceles triangle, there are three sides: two sides of equal length and one distinct side. Our task is to identify what the equal sides are called.

To address this, let's review the basic properties of an isosceles triangle:

  • An isosceles triangle is defined as a triangle with at least two sides of equal length.
  • The side that is different in length from the other two is usually called the "base" of the triangle.
  • The two equal sides of an isosceles triangle are referred to as the "legs."

Therefore, each of the two equal sides in an isosceles triangle is called a "leg."

In our problem, we confirm that the correct terminology for these two equal sides is indeed "legs," distinguishing them from the "base," which is the unequal side. This aligns with both the typical definitions and properties of an isosceles triangle.

Thus, the equal sides in an isosceles triangle are known as legs.

Answer:

Legs

Frequently Asked Questions

How do you identify an isosceles triangle?

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An isosceles triangle has two sides of equal length called legs. You can identify it by looking for two equal sides or two equal angles opposite those sides.

What are base angles in an isosceles triangle?

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Base angles are the two angles adjacent to the base (the unequal side) of an isosceles triangle. These angles are always equal to each other and are always acute angles (less than 90°).

How do you find the vertex angle of an isosceles triangle?

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To find the vertex angle: 1) Add the two base angles together, 2) Subtract this sum from 180°, 3) The result is your vertex angle. Remember that all triangle angles sum to 180°.

Can an isosceles triangle have a right angle?

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Yes, an isosceles triangle can have a right angle (90°) at the vertex. In this case, the two base angles would each measure 45°, since 180° - 90° = 90°, and 90° ÷ 2 = 45°.

What is the difference between legs and base in isosceles triangles?

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The legs are the two equal sides of an isosceles triangle, while the base is the third side that has a different length. The vertex angle lies between the two legs.

How do you solve isosceles triangle angle problems?

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Use these key properties: 1) Base angles are equal, 2) All angles sum to 180°, 3) If you know one base angle, the other base angle is the same, 4) Subtract the sum of base angles from 180° to find the vertex angle.

Can base angles in an isosceles triangle be obtuse?

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No, base angles in an isosceles triangle cannot be obtuse (greater than 90°). If they were obtuse, their sum would exceed 180°, which is impossible since all three angles must sum to exactly 180°.

What are the types of isosceles triangles?

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Isosceles triangles are classified by their vertex angle: 1) Acute isosceles - vertex angle less than 90°, 2) Right isosceles - vertex angle equals 90°, 3) Obtuse isosceles - vertex angle greater than 90°.

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