What is the alternate exterior angle conjecture?
What is the alternate exterior angle conjecture?
The Alternate Exterior Angle Conjecture states: “If two parallel lines are intersected by a transversal, then alternate exterior angles are congruent.” a.
What is a conjecture angle?
Conjecture (Corresponding Angles Conjecture ): If two parallel lines are cut by a transversal, the corresponding angles are congruent. Conjecture (Alternate Interior Angles Conjecture ): If two parallel lines are cut by a transversal, the alternate interior angles are congruent.
What does AIA conjecture mean in math?
C-3b Alternate Interior Angles Conjecture, or AIA Conjecture If two parallel lines are cut by. a transversal, then alternate interior angles are congruent. (
What is alternate exterior angle with example?
When two lines are crossed by another line (called the Transversal): Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal. In this example, these are two pairs of Alternate Exterior Angles: a and h.
How do you calculate alternate exterior?
To find alternate exterior angles, look at that outside space for each crossed line, on different sides of the transversal.
- We hope you said ∠1 , ∠2 , ∠7 , and ∠8 are the exterior angles.
- To find the partner of ∠2 , look on the other side of the transversal.
- If we know that ∠8 measures 130° , what is the measure of ∠1?
What does the exterior angle theorem state?
The exterior angle theorem is Proposition 1.16 in Euclid’s Elements, which states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.
What is example of alternate exterior angle?
What do alternate exterior angles add up to?
If the transversal cuts across parallel lines (the usual case) then exterior angles are supplementary (add to 180°). So in the figure above, as you move points A or B, the two angles shown always add to 180°.
What are the alternate exterior angles?
In this example, these are two pairs of Alternate Exterior Angles: To help you remember: the angle pairs are on Alternate sides of the Transversal, and they are on the Exterior of the two crossed lines. Parallel Lines. When the two lines being crossed are Parallel Lines the Alternate Exterior Angles are equal.
What is the converse of the alternate exterior angle theorem?
The converse of alternate exterior angle theorem states that, if the alternate exterior angles formed by two lines, which are cut by a transversal, are congruent, then the lines are parallel. Hence, in the above figure, if it is given that ∠1 = ∠7 then line AB || line CD.
Are alternate exterior angles congruent when the lines are parallel?
Alternate exterior angles are congruent when the lines are parallel. If the lines are not parallel, the alternate exterior angles are not congruent.
How many pairs of alternate exterior angles does a transversal have?
With each pair of alternate exterior angles, both angles are outside the parallel lines and on opposite (alternate) sides of the transversal. There are thus two pairs of these angles.
