warm up given: diagram as shown prove:
TRANSCRIPT
Warm UpWarm UpGiven: Diagram as shownProve: <1 congruent <3
Hint: Think of Supplementary Angles!
3. <DBE is a straight < 3. Same as 14. <2 is supp to <3 4. Same as 25. <1 congruent to <3 5. Supplements of the
same < are congruent
2.8 Vertical Angles2.8 Vertical Angles
http://www.phschool.com/atschool/academy123/html/bbapplet_wl-problem-431584.html
Opposite Rays:
Two collinear rays that have a common endpoint and extend in different directions
B A C
Ray AB and ray AC are opposite rays.
B A C D
Ray BA and Ray CD are not opposite rays.
V UX Y
Ray UV and Ray XY are not opposite rays. NO common end point.
Vertical Angles: when ever two lines intersect, two pairs of vertical angles are formed.
You can assume Vertical Angles!
Def: Two angles are vertical angles if the rays forming the sides of one angle and the rays forming the sides of the other are opposite rays.
A BE
D C
1 24
3
<1 &<2; <3 & <4 are vertical angles.
T18: Vertical angles are congruent.
5
67
Given: diagram
Prove <5 congruent to <7
Hint: use supplementary angles
2.4 problem2.4 problem
Therefore <5 <7
Given: <2 congruent to <3
Prove: <1 congruent to <3
123
45
6
m<4 = 2x +5
m<5 = x + 30
Find the m<4 and m<6
Vertical angles are congruent so just set them equal to each other and solve for x.
REMEMBER to plug x back in to find the angle.
The measure of <6 = 180-55
= 125