Chapter 1.4 – 1.7 By: Lindsey Harris and Lydia Pappas Click Here For the Best Website Ever!

Overview  1.4- Perpendicular and Parallel Lines  1.5- Special Points In Triangles  1.6- Motion in Geometry  1.7- Motion in the Coordinate Plane  1.4- Perpendicular and Parallel Lines  1.5- Special Points In Triangles  1.6- Motion in Geometry  1.7- Motion in the Coordinate Plane

1.4- Perpendicular and Parallel Lines If two coplanar lines are perpendicular to the same line, then the lines are parallel.

1.4- Perpendicular and Parallel Lines The perpendicular segment is the shortest distance between a point and a line.

1.4- Perpendicular and Parallel Lines  The distance from a point on the perpendicular bisector to the end points of the segment are equal.

1.4- Perpendicular and Parallel Lines  The distances from a point on the angle bisector to the sides of the angle are equal.

1.5 Special Points in Triangles Perpendicular bisector of a triangle is a line, ray or segment that is perpendicular to a side of the triangle at the midpoint of the side The point of concurrency of the perpendicular bisectors of a triangle is called the circumcenter. Acute Triangle- Inside Obtuse Triangle- Outside Right Triangle- ON A circle can be circumscribed around the triangle with the center at the circumcenter.

1.5 Special Points in Triangles Angle Bisectors cut the angle in half The point of concurrency of the angle bisectors is called the incenter. A circle can be inscribed in a triangle with the center at the incenter. Angle Bisectors cut the angle in half The point of concurrency of the angle bisectors is called the incenter. A circle can be inscribed in a triangle with the center at the incenter.

1.5 Special Points in Triangles Altitude of a triangle is the perpendicular segment from the vertex to the opposite side or to the line that contains the opposite side. *An altitude can lie inside, on, or outside the triangle. The point of concurrency of the altitudes is called the orthocenter. Altitude of a triangle is the perpendicular segment from the vertex to the opposite side or to the line that contains the opposite side. *An altitude can lie inside, on, or outside the triangle. The point of concurrency of the altitudes is called the orthocenter.

1.5 Special Points in Triangles A median of a triangle is a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side. The point of concurrency of the medians is called the centroid.

1.6- Motion in Geometry  Translation: Where every point moves in a straight line, same distance, and same direction.  Reflection: Every point is flipped across the line of reflection.  Rotation: Every point moves around a given point called the center of rotation.  Translation: Where every point moves in a straight line, same distance, and same direction.  Reflection: Every point is flipped across the line of reflection.  Rotation: Every point moves around a given point called the center of rotation.

1.7- Rotation in the Coordinate Plane RHorizontal Translation of H units: (x+H, y). RVertical Translation of V units: (x, y+V). RReflection across y axis: (-x,y). RReflection across x axis: (x,-y). R180° Rotation about the origin: (-x,- y). RHorizontal Translation of H units: (x+H, y). RVertical Translation of V units: (x, y+V). RReflection across y axis: (-x,y). RReflection across x axis: (x,-y). R180° Rotation about the origin: (-x,- y).

Practice Problems: k1) True or false. This motion demonstrates reflection.

Practice Problems: Name the points for the image of triangle ABC (8, -2) (4, 4) (0, -2) if the horizontal translation unit is 5. Vertical translation if unit is 3?

Practice Problems: If triangle ABC (3,6) (5, 2) (-2, 1) is reflected across the x axis what will the new points be. Reflected across the y axis?

Practice Problems: If triangle ABC (-5, 2) (-2, 6) (-3, -4) has a 180° rotation about the origin what are its new points?

The End Good luck on your final!