4th Grade Math
Geometry
Unit 6
Lesson 1: Angles and Lines
Acute, Right, and Obtuse Angles
Acute Angles: Acute angles are angles that are below 90 degrees.
Right Angles: Right angles are angles that are exactly 90 degrees.
Obtuse Angles: Obtuse angles are angles that are above 90 degrees.
Lines, Line Segments, and Rays
Line Segments:
Line segments, unlike lines, have two endpoints. A line segment is a small part of a line that is infinite. Its length is able to be measured. ( ⎯⎯ )
Ray:
A ray has one endpoint and one end that goes on forever. Unlike a line segment, it can not be measured. (→)
Lines:
A line is an infinite collection of points that extends into two directions. There are no endpoints on a line. (←→)
Parallel, Perpendicular, and Intersecting Lines
Parallel Lines: Parallel lines are lines that never intersect. The symbol for them is ||.
Perpendicular Lines: Perpendincular lines are lines that cross and create a right angle (an angle of 90 degrees). ⊥ is the symbol for parallel lines
Intersecting Lines: Lines are intersecting when they cross at a point. The point where they intersect is called the point of intersection
Lesson Two: Shapes
2-Dimensional and 3-Dimensional Shapes
Squares are 2-D shapes that have four equal right angles, and four equal sides. Perpendicular lines make the 4 right angles. There are two pairs of parallel lines and 4 perpendicular lines. Squares are a shape that have both parallel and perpendicular lines. The 3-D version is a cube.
Triangles- You can classify triangles by the angles that they have!
If a triangle has a right angle, it is a right triangle!
If a triangle has an obtuse angle, it is an obtuse triangle!
If a triangle has three acute angles, it is an acute angle!
Quadrilaterals- Quadrilaterals are shapes that have four sides and four angles. Some regular quadrilaterals are squares, rectangles, trapezoids, parallelograms, rhombuses, and kites.
Classifying Quadrilaterals:
Trapezoid- One pair of parallel lines
Parallelogram- Two pairs of parallel lines
Rhombus- Two pairs of parallel lines, all equal sides
Rectangle- Four right angles, two pairs of equal sides- not all equal
Square- Four right angles and four equal sides
Lesson 3: Lines of Symmetry
Lines of symmetry divide a shape or image into two equal halves. The line of symmetry divides it into two halves that mirror each other.
Lines of symmetry must be drawn to exactly cut a shape into equal halves.
Sometimes a shape has no lines of symmetry, and sometimes it has many. For example, a parallelogram has no lines of symmetry while circles have an infinite amount of lines of symmetry!
When counting lines of symmetry, remember that a line of symmetry MUST divide the shape into mirroring halves!