Given: Circle O with diameter LN and inscribed angle LMN Prove: is a right angle. What is the missing reason in step 5? Statemen
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<u>Question 4</u>
1) bisects
,
, and
(given)
2) (an angle bisector splits an angle into two congruent parts)
3) and
are right angles (perpendicular lines form right angles)
4) and
are right triangles (a triangle with a right angle is a right triangle)
5) (reflexive property)
6) (HA)
<u>Question 5</u>
1) and
are right angles,
,
is the midpoint of
(given)
2) and
are right triangles (a triangle with a right angle is a right triangle)
3) (a midpoint splits a segment into two congruent parts)
4) (HA)
5) (CPCTC)
<u>Question 6</u>
1) and
are right angles,
bisects
(given)
2) (reflexive property)
3) (an angle bisector splits an angle into two congruent parts)
4) and
are right triangles (a triangle with a right angle is a right triangle)
5) (HA)
6) (CPCTC)
7) bisects
(if a segment splits an angle into two congruent parts, it is an angle bisector)
<u>Question 7</u>
1) and
are right angles,
(given)
2) and
are right triangles (definition of a right triangle)
3) (vertical angles are congruent)
4) (transitive property of congruence)
5) (reflexive property)
6) (HA theorem)
7) (CPCTC)
8) bisects
(definition of bisector of an angle)