Isosceles triangle
An isosceles triangle is a triangle with at least two sides of equal length and at least two angles of equal measure. The equal angles are called base angles and sit opposite the equal sides. For example, a triangle with angles of 70, 70, and 40 degrees is isosceles. This concept is covered in Chapter 7 of Saxon Math Course 2 for 7th grade math and connects to broader geometry topics like triangle classification, symmetry, and angle relationships that students use throughout middle and high school math.
Key Concepts
Property An isosceles triangle has at least two sides of the same length and at least two angles of the same measure.
Examples A triangle with angles measuring $70^\circ$, $70^\circ$, and $40^\circ$ is an isosceles triangle. In $\triangle ABC$, if side $\overline{AB}$ is the same length as side $\overline{AC}$, then $\angle C$ is equal to $\angle B$. An isosceles right triangle has one $90^\circ$ angle and two $45^\circ$ angles.
Explanation Isosceles triangles are all about pairs! If a triangle has two identical sides, then the angles sitting opposite those sides are also twins. It’s a geometric two for one special on sides and angles.
Common Questions
What is an isosceles triangle?
An isosceles triangle has at least two sides of equal length. The two equal sides are called legs, and the third side is the base. The angles opposite the equal sides, called base angles, are also equal in measure.
How do you identify an isosceles triangle?
Look for two sides with the same length or two angles with the same measure. If a triangle has angles of 70, 70, and 40 degrees, it is isosceles because two angles are equal. Tick marks on a diagram indicate equal sides.
What is the difference between isosceles and equilateral triangles?
An equilateral triangle has all three sides equal and all angles measuring 60 degrees. An isosceles triangle has at least two equal sides. Every equilateral triangle is technically isosceles, but not every isosceles triangle is equilateral.
How do you find the missing angle of an isosceles triangle?
Since the three angles sum to 180 degrees and two base angles are equal, if you know one base angle, double it and subtract from 180 to find the vertex angle. If the vertex angle is 40 degrees, each base angle is (180 - 40) / 2 = 70 degrees.
Does an isosceles triangle have a line of symmetry?
Yes, an isosceles triangle has exactly one line of symmetry that runs from the vertex angle to the midpoint of the base. This line bisects the vertex angle and the base perpendicularly.
When do students learn about isosceles triangles?
Isosceles triangles are introduced in elementary geometry and studied more formally in 7th grade math. Saxon Math Course 2 covers them in Chapter 7 alongside other triangle classifications.