3.6 Perpendiculars & Distance4.1 Classifying Triangles

First & Last NameFebruary 7, 2014

______Block

• The distance from a line to a point not on the line is the length of the segment perpendicular to the line from the point.

C

BA

1. Draw the segment that represents the distance from P to AB.

P

A B

• By definition, two parallel lines do not intersect. An alternate definition states that two lines in a plane are parallel if they are everywhere equidistant.

• The distance between two parallel lines is the distance between one of the lines and any point on the other line.

• Theorem: In a plane, if two lines are equidistant from a third line, then the two lines are parallel to each other.

2. Find the distance between the parallel lines x=4 and x=-2.

3. Find the distance between the parallel lines y=8 and y=-5.

4. Find the distance between the parallel

lines l and m whose equations are and ,respectively.

5. Find the distance from the line to the point .

Classifying Triangles by Angles

• Acute Triangle: all of the angles are acute

• Obtuse Triangle: one angle is obtuse

• Right Triangle: one angle is right

• Equiangular Triangle: an acute triangle with all angles congruent

Classifying Triangles by Sides

• Scalene Triangle: no two sides are congruent

• Isosceles Triangle: at least two sides are congruent

• Equilateral Triangle: all of the sides are congruent

6. Identify the indicated triangle in the figure.a. Isosceles triangles

b. Scalene triangles

7. Find x and the measure of each side of equilateral triangle RST if

8. The points C(2,2), E(-5,3), and D(3,9) form a triangle. Find the measures of each side and classify the triangle by sides.

Exit Slip1. Find the distance

between each pair of parallel lines .

2. Draw a triangle that is isosceles and right.

3. Find the measures of the sides of triangle TWZ with vertices at T(2,6), W(4, -5), and Z(-3,0). Classify the triangle.

4. Find the length of each side.

J

M

Nx-2

3x-92x-5