Download Angles

Lesson 5.1 – Measuring and Drawing Angles
Drawing Angles
1. Construct a ray and label the vertex
2. Place protractor guide over the vertex
3. Starting at zero side, find the point for the measurement
4. Mark the point and draw another ray going through it
Angles:
 Ray – begins with and endpoint and extends infinitely in one direction
 Angle – formed by two rays with a common endpoint
 Vertex – the endpoint of an angle
Naming Angles:
 Angle symbol and a letter or number
 Angle symbol and the vertex label
 Angle symbol and three letters (point on ray, vertex, point on other ray)
____________
__________
__________
Angle Types:
 Acute – greater than 0° degrees and less than 90°
 Right – exactly 90°, or a square corner
 Obtuse - greater than 90° degrees and less than 180°
 Straight - exactly 180°, or a line
 Reflex – greater than 180° degrees and less than 360°
_____________
Lesson 5.2 – Reasoning with Angle Measures
Angles
 Supplementary Angles – two or more angles that equal 180°
 Complementary Angles – two or more angles that equal 90°
 Adjacent Angles – angles sharing a common side (vertex, ray)
 Vertical (Opposite) Angles – congruent angles formed where 2 lines intersect
Angle Reasoning Rules
 Triangle – sum of angles equals 180°
 Parallelogram – sum of angle measurements equals 360°
 Polygons – count how many triangles are in it and multiply by 180°
 Opposite angles – congruent to one another
 Perpendicular Lines create 4 right angles
Lesson 5.9 – Parallel Lines, Angle Relationships
Parallel Lines – lines that never meet; always the same distance apart
Transversal – line that crosses over parallel lines

adjacent angles are supplementary, or total 180°

Two pairs of vertical angles at each intersection
Corresponding angles – created when angle measurements “slide” on transversal
Lesson 5.10 – Parallelograms
Parallelogram
 Formed by two pairs of parallel lines
Terms
 Consecutive Angles – pairs of angles next to one another in parallelograms
 Opposite Interior Angles – angles in opposite corners of parallelogram
 Opposite Sides – sides formed by parallel lines
Parallelogram Properties
 Opposite side pairs are parallel
 Opposite sides are congruent (same length)
 Opposite Interior angles are congruent (same degree measure)
 The sum of consecutive angle pairs is 180°