When two rays have the same endpoint, an angle is created.
Here, BA−→− and BC−→− meet to form an angle. An angle is labeled with an “∠” symbol in front of the three letters used to label it. This angle can be labeled ∠ABC or ∠CBA. Always put the vertex (the common endpoint of the two rays) in the middle of the three points. It doesn’t matter which side point is written first.
An angle bisector is a ray that divides an angle into two congruent angles, each having a measure exactly half of the original angle. Every angle has exactly one angle bisector.
BD¯¯¯¯¯¯¯¯ is the angle bisector of ∠ABC
∠ABDm∠ABD≅∠DBC=12m∠ABC
Label equal angles with angle markings, as shown below.
Investigation: Constructing an Angle Bisector
Draw an angle on your paper. Make sure one side is horizontal.
Place the pointer on the vertex. Draw an arc that intersects both sides.
Move the pointer to the arc intersection with the horizontal side. Make a second arc mark on the interior of the angle. Repeat on the other side. Make sure they intersect.
Connect the arc intersections from #3 with the vertex of the angle.
Answers & Comments
Answer:
Step-by-sCongruent Angles and Angle Bisectors
When two rays have the same endpoint, an angle is created.
Here, BA−→− and BC−→− meet to form an angle. An angle is labeled with an “∠” symbol in front of the three letters used to label it. This angle can be labeled ∠ABC or ∠CBA. Always put the vertex (the common endpoint of the two rays) in the middle of the three points. It doesn’t matter which side point is written first.
An angle bisector is a ray that divides an angle into two congruent angles, each having a measure exactly half of the original angle. Every angle has exactly one angle bisector.
BD¯¯¯¯¯¯¯¯ is the angle bisector of ∠ABC
∠ABDm∠ABD≅∠DBC=12m∠ABC
Label equal angles with angle markings, as shown below.
Investigation: Constructing an Angle Bisector
Draw an angle on your paper. Make sure one side is horizontal.
Place the pointer on the vertex. Draw an arc that intersects both sides.
Move the pointer to the arc intersection with the horizontal side. Make a second arc mark on the interior of the angle. Repeat on the other side. Make sure they intersect.
Connect the arc intersections from #3 with the vertex of the angle.
tep explanation: