Two-Dimensional Geometry Designing Triangles and Angle Relationships Shapes and Designs Two-Dimensional Geometry Designing Triangles and Angle Relationships

Protractor and Compass How to use Line up the middle mark on protractor with the vertex of the angle Make sure bottom of protractor is on one ray or side of angle Count up from zero – this is either inside or out side depending on the direction you are going Compass Measure pointy end to pencil for how long you want line Put pointy end where you want center/vertex Swing arc, this represents the segment and all the locations it could go

Practice Read angles from worksheet Measure angles on the back

Building Triangles Using side lengths to determine if they make a triangle Using side lengths and angles to determine if they make a triangle

Given the side lengths try and draw a triangle All are cm – how many different triangles can you make 4, 5, 10 4, 5, 8 What do you notice about the triangles that you could make and the side lengths given?

Given the measurements draw a triangle Remember how triangles are name – so order does matter with some of the sides and angles How many triangles were you able to construct with the dimensions? What are some conclusions you can make?

Angle Measurements and Properties Determining angle measurements using angle properties

Angle Properties Complementary Angles Angles add to 90 degrees Supplementary Angles Angles add to 180 degree Congruent angles exactly the same measure Vertical Angles formed from 2 intersecting lines, rays or segments They do not share a side, are across from each other They are congruent Linear Pairs supplementary angles that share a side and a vertex (adjacent) Polygon Angles Sum of the interior angles 180(n-2) Sum of exterior angles always 360 Exterior Angle property of a triangle It is supplementary to in the adjacent interior angles (linear pair) Is equal to the sum of the angles it does not touch

Examples

Parallel lines and Transversals Angles properties associated with parallel lines

Terms Parallel lines Lines that never touch, same slope Transversal Line that intersects a pair of parallel lines Angles that will be discussed – these are all pairs of angles Corresponding angles Alternate Interior angles Alternate Exterior angles Same Side Interior Angles

Interior Angles – angles that are between the two lines that the transversal crosses Exterior Angles – angles outside the two lines that the transversal crosses

4 Main properties with Parallel lines and Transversals Same side of transversal, nonadjacent, one interior and one exterior, congruent if lines are parallel Corresponding Angles Alternate Interior Angles Alternate Exterior Angles Same Side Interior Angles Both interior angles, opposite sides of transversal, nonadjacent, congruent in lines are parallel Both exterior, opposite sides of the transversal, nonadjacent, congruent if lines are parallel Both Interior, same side of the transversal, supplementary if lines are parallel

Example

Example