What if you were presented with an equilateral triangle and told that its sides measure x, y, and 8? What could you conclude about x and y? After completing this Concept, you'll be able to apply important properties about equilateral triangles to help you solve problems like this one.
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All sides in an equilateral triangle have the same length. One important property of equilateral triangles is that all of their angles are congruent (and thus
Equilateral Triangle Theorem: All equilateral triangles are also equiangular. Furthermore, all equiangular triangles are also equilateral.
Find the value of
Solution: Because this is an equilateral triangle
Find the values of
The markings show that this is an equilateral triangle since all sides are congruent. This means all sides must equal
Two sides of an equilateral triangle are
The two given sides must be equal because this is an equilateral triangle. Write and solve the equation for
To figure out how long each side is, plug in
1. Find the measure of
2. Fill in the proof:
|2.||2. Base Angles Theorem|
|3.||3. Base Angles Theorem|
|4.||4. Transitive PoC|
3. True or false: All equilateral triangles are isosceles triangles.
1. The markings show that all angles are congruent. Since all three angles must add up to
||2. Base Angles Theorem|
||3. Base Angles Theorem|
||4. Transitive PoC|
||5. Definition of equiangular.|
3. This statement is true. The definition of an isosceles triangle is a triangle with at least two congruent sides. Since all equilateral triangles have three congruent sides, they fit the definition of an isosceles triangle.
The following triangles are equilateral triangles. Solve for the unknown variables.
- Find the measures of
Answers for Explore More Problems
To view the Explore More answers, open this PDF file and look for section 4.11.