10. - DBE - 150
Given: ARST
10
Prove: m2 1 + m2 2 + m 2 3 = 180
The proof is -
Statement
a. 1. Through
T draw
11 RS
Reason
1. Ausalary
line
2. Given
3. Definition of
isosceles
4. Definition of
rt
5. Base L's of
isosceles =
6. Acute L's of rt
A are comple-
mentary
7. Angle
Reason
Statement
1. Auxiliary b. Through
line
T draw
XY 11 RS
2 m LXTS
2. Exterior sides 2. t. isosceles
+ m 2 5 = 180 in opposite rays
ARST
3. m 2 XTS 3. Angle
3. KT = ST
m24
addition
+ m2 3
theorem
4 L 3 is rt
4. m 24-
4. Substitution
2 = 90
m 3
5. m Z1 =
m 2 5 = 180
m 22
5. m Z1 =
5. If lines,
6. L1, L2
m 24
then
are comple.
m 2 2 =
alternate
mentary
m 2 5
interior L's= 7. m2 1 + m 2
6. m 2 1+m 6. Substitution
+ m 3 = 180
2 2 + m 2 3 = 1801
Statement
Reason
Statement
c. 1. RST with
1. Given
d. 1. Through T draw
exterior z's
XY 11 RS
4 and 5
2. m 2 1 = m
2. m 2 1 +
2. Sum of
L 4, m 22
2 2 + m 2 3
measures
= m 2 5
= 180
of Z's of
A = 180
3. m Z3+ m
3. Exterior
3. mL XTS +
24+ m 2 5
sides in
m 2 5 = 180
= 180
opposite rays
4. m 2 XTS +
m 2 2 = 180
5. Z XTS =
L 4+ L3
6. L2+ 23
addition
theorem
Reason
1. Auxiliary
line
2. If two 11 lines
are cut by a
transversal,
then correspond-
ing L's are =
3. Exterior sides
in opposite rays
4. Substitution
5. Angle addition
theorem
6. Substitution
+ 24 = 180
32