(Preferably answered by tomorrow night - that's plenty of time.)
Ray OB is the bisector of angle AOC and ray OC is the bisector of angle BOD. m of angle AOC = 60. Find m of angle COD.
*m means "measure"
Write a proof in two-column form.
Given: ray DC is perpendicular to line BD; angle 1 is congruent to angle 2
Prove: ray BA is perpendicular to line BD
I have an image for the second problem, but they won't allow me to show links. ... )]= (Is there a remedy to this?)
Thank you guys so much in advance! =)
DC is perpendicular to BD. [Given]
Angle 2 = 90°. [Def. of perpendicular]
Angle 1 = angle 2. [Given]
Angle 1 = 90° [Transitive property of equality]
Therefore, BA is perpendicular to BD. [Def. of perpendicular]
To find the measure of angle COD, we can use the fact that the bisector of an angle divides it into two congruent angles.
Given: Ray OC is the bisector of angle BOD, and Ray OB is the bisector of angle AOC.
We are also given the measure of angle AOC as 60 degrees.
Step 1: Let x be the measure of angle BOC.
Step 2: Since Ray OC bisects angle BOD, we know that angle DOC and angle DOB are congruent, so angle DOB also has a measure of x degrees.
Step 3: Since Ray OB bisects angle AOC, we know that angle COB and angle COA are congruent. Since angle AOC has a measure of 60 degrees, angle COB also has a measure of 60 degrees.
Step 4: Using the properties of a triangle, we know that the sum of the angles in a triangle is 180 degrees. Therefore, angle BOC + angle COB + angle BOB = 180 degrees.
Step 5: Substitute the measures of the angles we know: x + 60 + x = 180.
Step 6: Simplify: 2x + 60 = 180.
Step 7: Subtract 60 from both sides: 2x = 120.
Step 8: Divide both sides by 2: x = 60.
Therefore, the measure of angle COD is x, which we found to be 60 degrees.
For the second problem, since you mentioned that you have an image that cannot be shared, I will describe a general approach to prove the given statement.
Given: Ray DC is perpendicular to line BD, and angle 1 is congruent to angle 2.
To prove: Ray BA is perpendicular to line BD.
Step 1: Start by assuming that Ray BA is not perpendicular to line BD.
Step 2: Show that this assumption leads to a contradiction or inconsistency.
Step 3: Use the fact that Ray DC is perpendicular to line BD to derive a contradiction or inconsistency.
Step 4: Conclude that the assumption made in Step 1 is false.
Step 5: Therefore, Ray BA must be perpendicular to line BD.
Since I am unable to see the provided image, this general approach should help guide you in constructing the proof. You can apply geometric properties, definitions, and theorems to establish the contradiction and conclude the desired result.