Angles and parallel lines (Pre-Algebra, Introducing geometry) – Mathplanet
When two lines intersect they form two pairs of opposite angles, A + C and B + D. Angles that are in the area between the parallel lines like angle 2 and 8. Relationship between sides and angles. In any triangle, the largest side and largest angle are opposite one another. In any triangle, the smallest side and. Practice telling whether two angles are supplementary, complementary, or vertical. Next tutorial. Angles between intersecting lines · Vertical angles review .
Ask the student to identify the measures of all other angles in the diagram. Making Progress The student is unable to clearly justify the relationship between the measures of the angles.
Examples of Student Work at this Level The student states that the angles in each angle pair have the same measure or are congruent. However, the student is unable to provide a justification.
Questions Eliciting Thinking How did you determine the angles are equal? Do you know the names of any of the special angle pairs in the diagram?
- Angles and parallel lines
- Justifying Angle Relationships
- Parallel Lines, and Pairs of Angles
Instructional Implications Ask the student to explain how he or she determined that the angle measures are congruent. Assist the student in developing an appropriate justification based on the approach the student took. For example, if the student used tracing paper to copy one angle and compare it to the other angle, help the student devise an appropriate explanation describing the rigid motions used to confirm the congruence of the angles.
Provide additional opportunities to justify the relationship between the measures of angles formed by parallel lines and a transversal. Assist the student in transitioning from using tracing paper to developing a logical argument.
Got It The student provides complete and correct responses to all components of the task.
Parallel Lines, and Pairs of Angles
Examples of Student Work at this Level The student states that the angles in each angle pair are the same measure or are congruent and provides an appropriate justification. For example, the student: Traces one of the angles and places it on top of the other angle so that the vertex and both sides of the one angle coincide with the vertex and both sides of the other angle. Logically reasons that vertical angles are congruent, and when two parallel lines are intersected by a transversal, the alternate interior angles are congruent.
For example, the student states that is congruent to since they are vertical and is congruent to since they are alternate interior or since it was just established in the previous problem and concludes that must be congruent to.
Questions Eliciting Thinking You used tracing paper to copy one angle and compare it to the other. What rigid motion might describe what you did? Do you know the name of this kind of angle pair? And the way you think about vertical angles is, imagine two lines crossing. So imagine two lines crossing, just like this. And they could literally be lines, and they're intersecting at a point. This is forming four angles, or you could imagine it's forming two sets of vertical angles.
So if this is the angle that you care about, it's a vertical angle, it's the one on the opposite side of the intersection. It's one of these angles that it is not adjacent to. So it would be this angle right over here.What is the Relation of an Exterior Angle of a Triangle with its Interior Angles?
Actually, what we already highlighted in magenta right over here. So this is angle DGB. Which could also be called angle BGD. These are obviously both referring to this angle up here.
Angle relationships example
Name an angle that forms a linear pair with the angle DFG. So we'll put this in a new color. Sorry, DGF, all of these should have G in the middle.
So linear pair with angle DGF, so that's this angle right over here.
So an angle that forms a linear pair will be an angle that is adjacent, where the two outer rays combined will form a line. So for example, if you combine angle DGF, which is this angle, and angle DGC, then their two outer rays form this entire line right over here.
So we could say angle DGC. Or, if you look at angle DFG, you could form a line this way. If you take angle AGF, so if you take this one, then the outer rays will form this line. So angle AGF would also work.