18
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Given: ZXOB
ZAOX
Prove: m/XOB = 90°
Statements
1. ZXOB ZAOX
2. ZXOB and ZAOX are supplementary
3. m/XOB + m/AOX = 180°
4. m/XOB = m/AOX
5.2m/XOB = 180°
6. m/XOB = 90°
Reasons
1. given
2. linear pair theorem
3. definition of supplementary angles
4. definition of congruence
5. substitution property of equality
6. division property of equality
Write the proof in a paragraph format.
Since AOB forms a line segment, ZXOB and ZAOX are supplementary by the
supplementary angles, m/XOB + m/AOX= 180°. Since it is given that ZXOB ZAOX, then m/XOB =
Applying the
then 2m/XOB = 180°. After dividing, m/XOB
= 90°
Reset
Next
. Using the definition of
m/AOX