Parallel Lines and Transversals
Pairs of opposite angles formed by intersecting lines
Vertical Angles
What does "congruent" mean?
Equal
What is the sum of the three interior angles in any triangle?
180 degrees
Any exterior angle is equal to the ___ of the two remote interior angles
Sum
Triangle ABC has angle measures 50 and 30. Triangle DEF has angle measures 30 and 100. Are the triangles similar?
Yes, 30+50+100=180
Angles in the same relative position (in matching corners)
Corresponding Angles
Congruent
If a triangle has a 110 degree angle and a 40 degree angle, how many degrees is the missing angle?
30 degrees
Any exterior angle is equal to the sum of its two ______ _______ angles
Remote Interior
Triangles ABC and DEF are similar. Triangle ABC has an angle measure of 45 while Triangle DEF has an angle measure of 25. What is the third angle missing from triangle ABC and DEF?
110 degrees
Angles outside the parallel lines and on opposite sides of the transversal are called:
Alternate Exterior Angles
Are vertical angles congruent or supplementary?
Congruent
If a straight angle is cut into 3 parts and one of the angles is 25 degrees and another is 50 degrees, how many degrees is the missing angle?
105 degrees
If the two remote interior angles of a triangle are 40 and 30, what is the measure of the exterior angle?
70
Triangle ABC has angle measures 90 and 20. Triangle DEF has angle measures 20 and 80. Are the triangles similar?
No, 90+20+80=190
Angles inside the parallel lines and on opposite sides of the transversal
Alternate Interior Angles
100
Could these angles create a triangle?
40 degrees, 90 degrees, 40 degrees
If the exterior angle is 120 degrees and one of the remote interior angles is 30 degrees, what is the measure of the other remote interior angle?
90 degrees
If one triangle has angles 50 and 30 and another triangle has angles 100 and 30, could they possibly be similar?
yes
Supplementary angles add up to:
180 degrees
If a transversal cuts a straight angle and one of the angles is 45 degrees, how many degrees is the other angle?
135
If a triangle has a right angle and a 30 degree angle, what is the measurement of the missing angle?
60 degrees
If a triangle has an exterior angle of 78 degrees and a remote interior angle of 30 degrees, what is the measure of the other remote interior angle?
48 degrees
If we know that 2 triangles are similar, we can set up ________________ in order to find the missing side length
Proportions