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2D Shapes Lines of symmetry Types of angles Regular polygonsHere you will learn about isosceles triangles, including what an isosceles triangle is and the properties of isosceles triangles.
Students first learn about triangles in kindergarten and 1 st grade in geometry with their work in reason with shapes and their attributes. They expand their knowledge of triangles as they progress through elementary school and into secondary school.
An isosceles triangle is a unique type of triangle because it has two equal (congruent) sides and two equal (congruent) angles.
Properties of an isosceles triangle:
The dashes on the sides and the angles of the triangle mean they are equal in measure or congruent.
The equal (congruent) angles of an isosceles triangle are called the base angles.
The base angles are opposite the equal (congruent) side lengths.
The unequal side (third side) of an isosceles triangle is often called the base of the triangle.
The unequal angle (third angle) of an isosceles triangle is called the vertex angle.
There are three different types of isosceles triangles.
Obtuse isosceles triangle  Acute isosceles triangle  Right isosceles triangle 

● Has 1 obtuse angle
 ● Has 3 acute angles
 ● Has 1 right angle

An isosceles triangle has \bf{1} line of symmetry. The line goes from the vertex to the exact middle of the base. The line of symmetry is perpendicular to the base of the isosceles triangle.
How does this apply to 4th grade and 5th grade math?
In order to identify isosceles triangles:
Assess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!
DOWNLOAD FREEAssess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!
DOWNLOAD FREEIs the triangle below an isosceles triangle?
An isosceles triangle is a triangle with two equal (congruent) sides and two equal (congruent) angles.
2Explain why the triangle fits or does not fit the definition.
This triangle is an isosceles triangle because it has two side lengths that are 12 \, cm each. So, the triangle has two equal (congruent) sides.
Is the isosceles triangle below a right isosceles triangle, obtuse isosceles triangle, or acute isosceles triangle?
Recall the definition.
An obtuse isosceles triangle is an isosceles triangle that has 1 obtuse angle.
An acute isosceles triangle is an isosceles triangle that has 3 acute angles.
A right isosceles triangle is an isosceles triangle that has 1 right angle (90^{\circ}).
Explain why the triangle fits or does not fit the definition.
The isosceles triangle shown has one 100^{\circ}, which is an obtuse angle. So, the triangle is an obtuse isosceles triangle.
Choose the triangle that is a right isosceles triangle.
Recall the definition.
A right isosceles triangle is an isosceles triangle with one right angle, (90^{\circ}).
Explain why the triangle fits or does not fit the definition.
Triangle A is not the right choice. Triangle A has 1 right angle, but it is not an isosceles triangle because there are no side lengths that are the same.
Triangle C is not the right choice. Triangle C is an isosceles triangle because it has two sides with lengths that are equal (congruent), but it is not a right triangle.
Triangle B is the correct choice because it has two side lengths that are equal (congruent) and it has a right angle, so it is a right isosceles triangle.
How many lines of symmetry does the triangle have?
Recall the definition.
Isosceles triangles have one line of symmetry going through the vertex angle to the exact middle of the base.
Explain why the triangle fits or does not fit the definition.
This isosceles triangle has 1 line of symmetry that goes through the vertex angle to the middle of the base of the triangle.
What type of isosceles triangle is shown in this image?
Recall the definition.
An obtuse isosceles triangle is an isosceles triangle that has 1 obtuse angle.
An acute isosceles triangle is an isosceles triangle that has 3 acute angles.
A right isosceles triangle is an isosceles triangle that has 1 right angle (90^{\circ}).
Explain why the triangle fits or does not fit the definition.
The banners in the photo appear to be acute isosceles triangles because the vertex angle and the base angles appear to be acute angles, greater than 0^{\circ} and less than 90^{\circ}.
What type of isosceles triangle does this photo represent?
Recall the definition.
An obtuse isosceles triangle is an isosceles triangle that has 1 obtuse angle.
An acute isosceles triangle is an isosceles triangle that has 3 acute angles.
A right isosceles triangle is an isosceles triangle that has 1 right angle (90^{\circ}).
Explain why the triangle fits or does not fit the definition.
The hanger appears to be an obtuse isosceles triangle because the vertex angle appears to be obtuse, greater than 90^{\circ} and less than 180^{\circ}.
1. Which of these diagrams shows an isosceles triangle?
The dash marks on the sides of the triangle indicate which lengths are equal. You need the triangle which has the same mark on two sides.
2. How many lines of symmetry does an isosceles triangle have?
An isosceles triangle only has one line of symmetry that cuts the triangle into two equal parts that are mirror images of each other.
The line of symmetry goes from the vertex angle to the middle point of the base.
3. Select the triangle that represents an obtuse isosceles triangle.
An obtuse isosceles triangle is an isosceles triangle that has 1 obtuse angle.
4. If a triangle has side measurements of 14 inches, 14 inches, and 19.8 inches and one angle that is 90^{\circ}, what type of triangle is it?
Isosceles triangle
Right isosceles triangle
Acute isosceles triangle
Right scalene triangle
Here is a drawing of the triangle with the given information.
The triangle has two side lengths that are equal in measure, and it also has a 90^{\circ}. So, the triangle is a right isosceles triangle.
5. Which photo represents an isosceles triangle?
An isosceles triangle has two equal sides and two equal angles.
This photo of the roof appears to be an isosceles triangle because of the two equal sides and the two equal angles.
6. Joey drew a picture of an isosceles triangle. Which set of angle measurements can be the angles of the triangle she drew?
An isosceles triangle has two equal (congruent) sides and two equal (congruent) angles.
So the angle measurements of the triangle Joey drew could be 70^{\circ}, 55^{\circ}, 55^{\circ}.
You can use the formula for finding the area of a triangle, which is a=\cfrac{1}{2} \cdot b \cdot h. The height of an isosceles triangle is a line segment that starts at the vertex angle and is perpendicular to the opposite side. The height is also known as the altitude of the triangle.
You can find the perimeter of an isosceles triangle the same way you would find the perimeter of any polygon, add up all the side lengths.
Only right isosceles triangles will have a hypotenuse. The hypotenuse is the longest side of a right triangle, so only right triangles have hypotenuses.
Trigonometry is the study of triangles where you will learn ratio relationships of right triangles such as sine, cosine, and tangent ratios. You will learn about trigonometry in high school.
You can only use the Pythagorean theorem on right isosceles triangles because the Pythagorean theorem only applies to right triangles.
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