Proving Lines Parallel
Two lines are crossed by a transversal. A pair of corresponding angles is congruent. What can you conclude about the lines?
The lines are parallel
What angle measure is formed when two lines are perpendicular?
90 degrees
Two angles of a triangle measure 55 and 65. Find the third angle.
60 degress
When parallel lines are crossed by a transversal, what is the relationship between corresponding angles?
They are congruent
An angle that is larger than 90 degrees is classified as what?
Obtuse
Alternate interior angles measure (5x+7) and (8x−20). If the lines are parallel, find xx.
x = 9
A line with slope 3/4 is perpendicular to a nonvertical line. What is the second line’s slope?
-4/3
Two angles in a triangle are 40 and 60 degrees. What type of triangle is this?
Acute
One angle formed by a transversal with parallel lines measures 68 degrees. Find the measure of its alternate interior angle.
68 degrees
What is an equiangular triangle?
A triangle with 3 equal angles
Same-side interior angles measure (3x+15) and (5x−3). Find x and determine whether these angles can prove the lines parallel.
x=21; the angles sum to 180, so the lines are parallel by the converse of the same-side interior angles theorem.
Find an equation for the line through (2,−1) and is perpendicular to y=−2/3x+5
y = 3/2x - 4
A triangle’s angles measure (2x), (3x+10), and (4x−10). Find x.
x = 20
Same-side interior angles measure (4x+12) and (6x−2). Find x.
x = 17
If two angles are supplementary and one of them measures 65, what is the measure of the other angle?
115
A transversal crosses two lines. One pair of alternate exterior angles is congruent. State the converse theorem that proves the lines are parallel.
The converse of the alternate exterior angles theorem.
A line has equation 4x−6y=12. Find the slope of a line perpendicular to it.
m = -2/3
An exterior angle of a triangle is 132. One remote interior angle is 57. Find the other remote interior angle.
Two alternate exterior angles measure (7x−9) and (4x+30). Find x and the angle measure.
x=13; each angle measures 82
What is the slope of the line passing through the points (2, 3) and (4, 7)
m = 2
A transversal crosses lines ℓ and m. Same-side interior angles measure (3x−4)and (5x+8). Find x and explain why the lines must be parallel.
x=22; the angles measure 62 and 118, so they are supplementary, and the lines are parallel by the converse of the same-side interior angles theorem.
The line through (1,4) and (k,10) is perpendicular to the line through (2,3) and (8,1). Find k.
k = 3
In a triangle, the angles measure (x+15), (2x−5), and (3x−10). Find x and the largest angle.
x=30; the largest angle is 80 degrees
Two parallel lines are crossed by a transversal. A pair of same-side interior angles measures (3x+18) and (5x−6). Find x and both angle measures.
x=21; the angles measure 81 and 99
Write an equation for a line that is parallel to
y = 2x - 7 and goes through the point (3,4)
y = 2x - 2