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

2. 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

3. Practice
Read angles from worksheet Measure angles on the back

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

5. 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?

6. 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?

7. Angle Measurements and Properties
Determining angle measurements using angle properties

8. 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

9. Examples

10. Parallel lines and Transversals
Angles properties associated with parallel lines

11. 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

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

13. 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

15. Example

16. Example