Parallel lines s and t are cut by a transversal, r.
Parallel lines s and t are cut by transversal r. Clockwise from top left, the angles formed with r and s are 1, 2, 3, 4; the angles formed with r and t are 5, 6, 7, 8.
If the measure of angle 1 is 68°, what is the measure of angle 5
Angle 1 and angle 5 are corresponding angles and are congruent since lines s and t are parallel. Therefore, if angle 1 is 68°, angle 5 is also 68°.
Parallel lines s and t are cut by a transversal r.
Parallel lines s and t are cut by transversal r. Clockwise from top left, the angles formed with r and s are 1, 2, 3, 4; the angles formed with r and t are 5, 6, 7, 8.
Which angles are alternate exterior angles?
Angles 1 and 8 are alternate exterior angles, as well as angles 2 and 7, and angles 3 and 6, and angles 4 and 5.
If Angle 8 is congruent to angle 10 and Angle 1 is congruent to angle 7, which describes all the lines that must be parallel?
Lines r and s are crossed by lines t and u to form 16 angles. Clockwise from top left, at the intersection of r and t, the angles are 1, 2, 3, 4; at the intersection of s and t, 5, 6, 7, 8; at the intersection of u and s, 9, 10, 11, 12; at the intersection of u and r, 13, 14, 15, 16.
If angle 8 is congruent to angle 10 and angle 1 is congruent to angle 7, then angles 8 and 10 are alternate interior angles, and angles 1 and 7 are also alternate interior angles. This means that lines r and u must be parallel, and lines s and t must be parallel.
For the second question: lines r and s are parallel since they have corresponding angles 1 and 5 that are congruent. Lines s and u are parallel since they have corresponding angles 10 and 6 that are congruent. Lines t and u are parallel since they have alternate interior angles 9 and 5 that are congruent. Therefore, all four lines (r, s, t, and u) must be parallel.
Which is enough information to prove that s is parallel to t?
Lines s and t are cut by transversal r to form 8 angles. Clockwise from top left, the angles formed with lines r and s are 1, 2, 3, 4; formed with lines r and t are 5, 6, 7, 8.
Angle 1 is congruent to angle 3
Angle 2 is congruent to angle 8
Angle 5 + angle 6 = 180 degrees
Angle 1 + angle 4 = 180 degrees
The information that is enough to prove that s is parallel to t is the fact that angle 2 is congruent to angle 8. These angles are alternate interior angles and must be congruent if lines s and t are parallel. Therefore, we can conclude that s is parallel to t.
Aliya lined up the interior angles of the triangle along line p below.
Triangle A B C.
When the measure of angle A increases in the triangle, what happens to angle A on line p?
It also increases.
It decreases.
It stays the same.
It may increase, or it may stay the same.
When the measure of angle A increases in the triangle, angle A on line p also increases. This is because angle A on line p is the corresponding angle to angle A in the triangle, and corresponding angles are congruent. As the angle in the triangle increases, the corresponding angle on line p also increases.
The two triangles below are similar.
mc004-1.jpg
What is the ratio of the corresponding side lengths?
4:9
4:2
26:26
4.5:2