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.

Key Parts:

  • Legs: The two equal sides
  • Base: The third side (different length)
  • Vertex angle: The angle between the two legs
  • Base angles: The two equal angles adjacent to the base

This fundamental property—that equal sides create equal opposite angles—makes isosceles triangles essential building blocks in geometry and forms the basis for the Isosceles Triangle Theorem.

A - Identification of an isosceles triangle

Detailed explanation

Practice Isosceles triangle

Test your knowledge with 20 quizzes

In a right triangle, the side opposite the right angle is called....?

Examples with solutions for Isosceles triangle

Step-by-step solutions included
Exercise #1

What kid of triangle is given in the drawing?

90°90°90°AAABBBCCC

Step-by-Step Solution

The measure of angle C is 90°, therefore it is a right angle.

If one of the angles of the triangle is right, it is a right triangle.

Answer:

Right triangle

Video Solution
Exercise #2

What kind of triangle is given in the drawing?

404040707070707070AAABBBCCC

Step-by-Step Solution

As all the angles of a triangle are less than 90° and the sum of the angles of a triangle equals 180°:

70+70+40=180 70+70+40=180

The triangle is isosceles.

Answer:

Isosceles triangle

Video Solution
Exercise #3

What kid of triangle is the following

393939107107107343434AAABBBCCC

Step-by-Step Solution

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°,

C=107 C=107

Furthermore, the sum of the angles of the given triangle is 180 degrees so it is indeed a triangle:

107+34+39=180 107+34+39=180

The triangle is obtuse.

Answer:

Obtuse Triangle

Video Solution
Exercise #4

What kind of triangle is given in the drawing?

999555999AAABBBCCC

Step-by-Step Solution

Given that sides AB and AC are both equal to 9, which means that the legs of the triangle are equal and the base BC is equal to 5,

Therefore, the triangle is isosceles.

Answer:

Isosceles triangle

Video Solution
Exercise #5

Which kind of triangle is given in the drawing?

666666666AAABBBCCC

Step-by-Step Solution

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.

Answer:

Equilateral triangle

Video Solution

Frequently Asked Questions

Everything you need to know about Isosceles triangle

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°.

More Isosceles triangle Questions

Click on any question to see the complete solution with step-by-step explanations

Types of Triangles

Parallel Line Geometry: Classifying Triangle ABC with Extended Side AE Right Triangle Area Problem: Solve for X When Area = 6 cm² Square Diagonal Properties: Classifying Triangles ABC and ACD Isosceles Triangle ABC with Parallel Line ED: Investigating Triangle Properties Triangle Classification: Identifying a Shape with Three 60° Angles

Continue Your Math Journey

Master Isosceles triangle first, then advance to these related topics that build on your fraction skills

Topics Learned in Later Sections

AreaThe sides or edges of a triangleTriangle HeightThe Sum of the Interior Angles of a TriangleExterior angles of a triangleTypes of TrianglesObtuse TriangleEquilateral triangleIdentification of an Isosceles TriangleScalene triangleAcute triangleThe Area of a TriangleArea of a right triangleArea of Isosceles TrianglesArea of a Scalene TriangleArea of Equilateral TrianglesAreas of Polygons for 7th GradeRight TriangleMedian in a triangleCenter of a Triangle - The Centroid - The Intersection Point of MediansHow do we calculate the area of complex shapes?How to calculate the area of a triangle using trigonometry?All terms in triangle calculationPerimeterTrianglePerimeter of a triangleHow do we calculate the perimeter of polygons?

Practice by Question Type

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