Chapter 5 Triangles Overview w ans

Chapter 5 Triangles      Name __________________

Classifying Triangles by their Angles

Acute Triangles – All angles are less than 90°

 

 

 

Obtuse Triangles – Has an angle greater than 90°

 

 

Right Triangles – Has a 90° angle 

 

Equiangular Triangles – All angles are equal(60°) all

Angles are equal, all side lengths are equal.

 

 

Classifying Triangles by their Sides 

 

Scalene Triangles – All sides are different lengths.

 

 

Isosceles Triangles – At least two sides are congruent (at least two angles will also be congruent)

 

 

Equilateral Triangles – All sides are equal lengths.

 

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In a triangle, the largest angle is across from the __longest______ side of a triangle.  List the angles from smallest to largest.

 

 

 

 

 

 

 

 

 

The smallest angle is across (opposite) from the ___shortest____ side of a triangle. List the sides from smallest to largest.

   

 

 

 

 

 

Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side of the triangle.

 

 

 

AB + BC > AC

AC + AB > BC

BC + AC > AB

 

 

 

 

 

 

 

 

Exterior Angles of a Triangle

 

 

 

Remote interior angles

 

 

A + B + C = 180

C + BCD = 180

 

The measure of an exterior angle of a triangle is equal to the _measure___ of the measures of the two __remote____ _interior____ ___angles____.

 

 

 

 

The Exterior Angle Inequality Theorem states that the measure of an exterior angle of a triangle is greater than the measure of either of its remote interior angles.

 

 

 

 

 

 

 

 For more detail information on constructions, see yesterday's post and view the websites listed.

 

                                                                                            Point of Concurrency

 

Angle Bisectors of a Triangle- Divides the Angles in half       

_Incenter_

 

Medians of a Triangle - From the vertex to the middle of the      ___Centroid______

opposite side      

 

Altitudes of a Triangle – Right angle with the opposite side,      ___Orthocenter___

through the vertex      

 

Perpendicular Bisectors of the sides of a Triangle – Bisect the      ___Circumcenter___

Sides of the triangle at a right angle 

 

 

 

Triangle Congruence Postulates

Angle-Side-Angle

 

  

 

Side-Side-Side

 

    

 

Side-Angle-Side

 

 

  

 

Angle-Angle-Side

   

 

Hypotenuse-Leg