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Name: _______________________________________________________
Date: ______________________
Period: _________
Chapter 11B: Coordinate Geometry Triangle Proofs
Topic 1: Classifying Triangles
Recall the classifications of triangles:
By Sides:



Scalene Triangle:
All three sides of the triangle have different lengths.
Isosceles Triangle:
Two of the three sides of the triangle have the same length.
Equilateral Triangle: All three sides of the triangle have the same length.
To classify any triangle by its SIDES use: _________________________________________
By Angles:



Right Triangle:
Acute Triangle:
Obtuse Triangle:
One right angle
All acute angles
One obtuse angle
To classify a RIGHT triangle use: _____________________________________________
Then
Practice Examples:
1) The coordinates of the vertices of
and
Show that
_______________________________________________
are
is scalene.
Name: _______________________________________________________
Date: ______________________
2) Given ∆HIJ with
and
. Using coordinate
geometry prove that ∆HIJ is an isosceles triangle.
3) If the vertices of
are
show that it is a right triangle.
and
Period: _________
Name: _______________________________________________________
4) If the vertices of
classify the triangle.
are
and
5) The coordinates of the vertices of
are
and
Using coordinate geometry prove
that
is an isosceles right triangle.
Date: ______________________
Period: _________
Name: _______________________________________________________
Date: ______________________
Chapter 11B: Coordinate Geometry Triangle Proofs
Topic 1 Homework
1) The coordinates of the vertices of
and
Show that
are
is a scalene triangle.
2) If the vertices of
are
and
show that
is not an isosceles triangle.
Period: _________
Name: _______________________________________________________
3) If the coordinates of the vertices of
are
and
Using coordinate geometry
classify the triangle.
4.) The coordinates of the vertices of
are
and
Using coordinate geometry
prove that
is an isosceles right triangle.
Date: ______________________
Period: _________
Name: _______________________________________________________
Date: ______________________
Period: _________
5.) If the coordinates of the vertices of
are
and
Classify the triangle by side and angle.
Extra examples if you need more practice
1) The coordinates of the vertices of
triangle.
are
and
. Show that
2) If the coordinates of the vertices of
classify the triangle.
are
3) If the coordinates of the vertices of
triangle.
are
and
. Show that
4) If the coordinates of the vertices of
classify the triangle.
are
and
. Using coordinate geometry
5) If
and
, classify the triangle.
has the vertices
6) If the vertices of
are
and
and
is a scalene
show that
. Using coordinate geometry
is an isosceles
is an isosceles right triangle.
Name: _______________________________________________________
Coordinate Geometry Triangle Proofs (HW)
1)
2)
3)
4)
Date: ______________________
Period: _________
4.)
5.)
1)
2)
5)
6)
3)
4)