4.11. Equilateral Triangles http://www.ck12.org
( 2 x+ 5 )◦+( 2 x+ 5 )◦+( 3 x− 5 )◦= 180 ◦
( 7 x+ 5 )◦= 180 ◦
7 x= 175 ◦
x= 25 ◦Example C
Two sides of an equilateral triangle are 2x+5 units andx+13 units. How long is each side of this triangle?
The two given sides must be equal because this is an equilateral triangle. Write and solve the equation forx.
2 x+ 5 =x+ 13
x= 8To figure out how long each side is, plug in 8 forxin either of the original expressions. 2( 8 )+ 5 =21. Each side is
21 units.
Watch this video for help with the Examples above.
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter4EquilateralTrianglesB
Concept Problem Revisited
Let’s focus on one tile. First, these triangles are all equilateral, so this is an equilateral hexagon (6 sided polygon).
Second, we now know that every equilateral triangle is also equiangular, so every triangle within this tile has 360◦
angles. This makes our equilateral hexagon also equiangular, with each angle measuring 120◦. Because there are 6
angles, the sum of the angles in a hexagon are 6. 120 ◦or 720◦. Finally, the point in the center of this tile, has 660◦
angles around it. That means there are 360◦around a point.
Vocabulary
Anisosceles triangleis a triangle that hasat leasttwo congruent sides. The congruent sides of the isosceles triangle
are called thelegs. The other side is called thebase. The angles between the base and the legs are calledbase angles
and are always congruent by theBase Angles Theorem. The angle made by the two legs is called thevertex angle.
Anequilateral triangleis a triangle with three congruent sides.Equiangularmeans all angles are congruent. All
equilateral triangles are equiangular.
Guided Practice
- Find the measure ofy.