1. CD is the bisector of Angle ACB, the measure of Angle A=46 and the measure of Angle B=82. Find the measure of Angle ACD. Justify your results.
2. If Shane is an athlete and he is salaried, then Shane is a professional. Shane is not a professional. Shane is an athlete. Which statement must be true?
A) Shane is an athlete, and he is salaried.
B) Shane is a professional or he is salaried
C) Shane is not salaried
D) Shane is not an athlete.
3. When the statement “If A, then B†is true, which statement must also be true?
A) If B, Then A
B) If not A, Then B
C) If not B, then A
D) If not B, then not A
4. DC and EF are parallel, M Angle EGH = (2x-5). And the Measure of Angle GBC = (3x-10). Determine the Measure of Angle ABC. Explain your reasoning.
5. If two triangles are congruent, then all of the corresponding parts are congruent. Write the converse; contra-positive; and the inverse.
6. In triangle ABC, AB=BC. If the Measure of Angle Y =112, what is the measure of Angle X, justify your results.
7. Which is the converse of the statement “If today is Thanksgiving, then there is no school�
A) If there is school, then today is not Thanksgiving.
B) If there is no school then today is Thanksgiving.
C) If today is Thanksgiving, then there is school.
D) If today is not Thanksgiving, then there is school.
8. Given OS bisects Angle TOP, OM is parallel to OP, the Measure of Angle MOT = (3x+3), and the Measure of Angle TOS = (2x+5), find the Measure of Angle TOP, Justify your results.
9. In Triangle SAT the Measure of Angle S = (2x-10), the Measure of Angle A is = to (x+15, and the Measure of Angle T = (4x-20). Describe Triangle SAT.
10. Find the Measure of Angle DBC if Measure of Angle ACB = (21x+36). The Measure of Angle FCG = (13x+42), and the Measure of Angle ADB = 83, justify your results.
Proofs
1. Since CD is the bisector of Angle ACB, we know for sure that Angle BCD is = to Angle DCA. There is a triangle in this drawing, which means that all three angles would have to total 180˚. We are given the measure of Angle A, and Angle B, the third angle (Angle BCA) would have to equal, the measure of Angles B, and A subtracted by 180, because all triangles have 180˚ total. After we get the measure of Angle BCA, you divide that Number by 2 because CD bisects Triangle ACD, and you are left with the measure of Angle DCA.
Answer- Measure of Angle DCA = 26˚
2. The very first sentence states that “If Shane is an athlete and he is salaried, then Shane is a professional.†The next part says “Shane is not a professional. Shane is an athlete.†The second sentence of the second part, states that he is an athlete, which is verifying what the first quote says (he is an athlete). Since nothing is said about Shane NOT being Salaried, then he must be salaried, which justifies, that Shane is an athlete and he is salaried.
Answer- A) Shane is an athlete, and he is salaried
3. If you say that A is = to B, then you have to assume that if it is not B, then it can’t be A; because A is = to B.
Answer – D) If not B, then not A.
4. Since the Angles EGH and GBC have nothing in common, we have to find another angle that we can use to figure out the Measure of Angle GBC, which will lead us to the measure of ABC. We know that linear pairs are all = to 180˚ so we can use this to find the Measure of the Angle of EGB, which takes us one step closer to figuring out the Angle of GBC, and onto Angle ABC. Since lines DC, and EF are parallel we can conclude that Angles EGB, and GBC, are alternate interior angles, which in turn proves Angles EGB, and GBC congruent. Now that we have the measure of Angle GBC, we can conclude that the Measure of Angle ABC is = to Measure of Angle GBC – 180.
Answer- 152.5˚
5. First we start out with the statement, “if two triangles are congruent, then all of the corresponding parts are congruent.†First we have to find the converse of this statement which is, “If P, then Q†which means you switch the hypothesis and the conclusion around. Next the inverse is almost the same thing except you negate the statement, which means you add a Not in, or you take a Not out. Next the contra-positive, which is switching AND negating the statement, and it would look like If not “P, then not Qâ€
Answer-
Converse: If all of the corresponding parts are congruent, then two triangles are congruent.
Inverse: If two triangles aren’t congruent, then the corresponding parts aren’t.
Contra-positive: If all of the corresponding parts aren’t congruent, then the two triangles aren’t congruent.
6. We are given the measurement of Angle Y, which is an exterior angle. Since this angle forms a linear pair with AC, we can subtract the measure of Angle Y by 180˚ to get the measure of Angle C. Also, the information AB=BC is given, this helps us, because when the two legs of a triangle are congruent, this means the 2 base angles are congruent; using this information we can conclude that Angle C is congruent to Angle A. and because a linear pair is formed from Angle X, and Angle A we can subtract the measure of Angle A, to get the measure of Angle X.
Answer- 112˚
7. The converse of a statement is the switching of the hypothesis (P) and the conclusion (Q). So naturally, the converse of “If today is Thanksgiving, then there is no school†would just be switching around the order in which you say it.
Answer- B) If there is no school, then today is Thanksgiving.
8. Since OS bisects Angle TOP we know angle TOP will be broken up into 2 = parts, and part of the given information is the Measure of Angle TOS, which gives us the other part of TOP. Also in the given information is the fact that OM is perpendicular to OP which creates a right angle at the vertex, which gives you 90˚ to = the measure of TOP to so you can get a single number.
Answer- 54˚
9. To get this answer all you have to do is add up all of the angles of the triangle, and divide that by 180˚ because there is 180˚ in a triangle. After you do this you have to plug in the number you get to each equation, and you can classify the triangle by its angles.
Answer- Scalene
10. We are given the Measure of Angle ACB, which is part of the triangle that contains the angle we need to find. We are also given the Measure of Angle FCG which is vertical to Angle ACB; this gives us something to find out a true ˚. Lastly we are given the Measure of Angle ABD which helps us find the Measure of Angle DBC because it is an exterior angle of Triangle DBC. Subtract the Measure of Angle ABD from 80 and you get the 2nd needed angle in the Triangle DBC. Add those to Numbers together and we are left with the measure of Angle DBC.
Answer- 82.5˚
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2. If Shane is an athlete and he is salaried, then Shane is a professional. Shane is not a professional. Shane is an athlete. Which statement must be true?
A) Shane is an athlete, and he is salaried.
B) Shane is a professional or he is salaried
C) Shane is not salaried
D) Shane is not an athlete.
3. When the statement “If A, then B†is true, which statement must also be true?
A) If B, Then A
B) If not A, Then B
C) If not B, then A
D) If not B, then not A
4. DC and EF are parallel, M Angle EGH = (2x-5). And the Measure of Angle GBC = (3x-10). Determine the Measure of Angle ABC. Explain your reasoning.
5. If two triangles are congruent, then all of the corresponding parts are congruent. Write the converse; contra-positive; and the inverse.
6. In triangle ABC, AB=BC. If the Measure of Angle Y =112, what is the measure of Angle X, justify your results.
7. Which is the converse of the statement “If today is Thanksgiving, then there is no school�
A) If there is school, then today is not Thanksgiving.
B) If there is no school then today is Thanksgiving.
C) If today is Thanksgiving, then there is school.
D) If today is not Thanksgiving, then there is school.
8. Given OS bisects Angle TOP, OM is parallel to OP, the Measure of Angle MOT = (3x+3), and the Measure of Angle TOS = (2x+5), find the Measure of Angle TOP, Justify your results.
9. In Triangle SAT the Measure of Angle S = (2x-10), the Measure of Angle A is = to (x+15, and the Measure of Angle T = (4x-20). Describe Triangle SAT.
10. Find the Measure of Angle DBC if Measure of Angle ACB = (21x+36). The Measure of Angle FCG = (13x+42), and the Measure of Angle ADB = 83, justify your results.
Proofs
1. Since CD is the bisector of Angle ACB, we know for sure that Angle BCD is = to Angle DCA. There is a triangle in this drawing, which means that all three angles would have to total 180˚. We are given the measure of Angle A, and Angle B, the third angle (Angle BCA) would have to equal, the measure of Angles B, and A subtracted by 180, because all triangles have 180˚ total. After we get the measure of Angle BCA, you divide that Number by 2 because CD bisects Triangle ACD, and you are left with the measure of Angle DCA.
Answer- Measure of Angle DCA = 26˚
2. The very first sentence states that “If Shane is an athlete and he is salaried, then Shane is a professional.†The next part says “Shane is not a professional. Shane is an athlete.†The second sentence of the second part, states that he is an athlete, which is verifying what the first quote says (he is an athlete). Since nothing is said about Shane NOT being Salaried, then he must be salaried, which justifies, that Shane is an athlete and he is salaried.
Answer- A) Shane is an athlete, and he is salaried
3. If you say that A is = to B, then you have to assume that if it is not B, then it can’t be A; because A is = to B.
Answer – D) If not B, then not A.
4. Since the Angles EGH and GBC have nothing in common, we have to find another angle that we can use to figure out the Measure of Angle GBC, which will lead us to the measure of ABC. We know that linear pairs are all = to 180˚ so we can use this to find the Measure of the Angle of EGB, which takes us one step closer to figuring out the Angle of GBC, and onto Angle ABC. Since lines DC, and EF are parallel we can conclude that Angles EGB, and GBC, are alternate interior angles, which in turn proves Angles EGB, and GBC congruent. Now that we have the measure of Angle GBC, we can conclude that the Measure of Angle ABC is = to Measure of Angle GBC – 180.
Answer- 152.5˚
5. First we start out with the statement, “if two triangles are congruent, then all of the corresponding parts are congruent.†First we have to find the converse of this statement which is, “If P, then Q†which means you switch the hypothesis and the conclusion around. Next the inverse is almost the same thing except you negate the statement, which means you add a Not in, or you take a Not out. Next the contra-positive, which is switching AND negating the statement, and it would look like If not “P, then not Qâ€
Answer-
Converse: If all of the corresponding parts are congruent, then two triangles are congruent.
Inverse: If two triangles aren’t congruent, then the corresponding parts aren’t.
Contra-positive: If all of the corresponding parts aren’t congruent, then the two triangles aren’t congruent.
6. We are given the measurement of Angle Y, which is an exterior angle. Since this angle forms a linear pair with AC, we can subtract the measure of Angle Y by 180˚ to get the measure of Angle C. Also, the information AB=BC is given, this helps us, because when the two legs of a triangle are congruent, this means the 2 base angles are congruent; using this information we can conclude that Angle C is congruent to Angle A. and because a linear pair is formed from Angle X, and Angle A we can subtract the measure of Angle A, to get the measure of Angle X.
Answer- 112˚
7. The converse of a statement is the switching of the hypothesis (P) and the conclusion (Q). So naturally, the converse of “If today is Thanksgiving, then there is no school†would just be switching around the order in which you say it.
Answer- B) If there is no school, then today is Thanksgiving.
8. Since OS bisects Angle TOP we know angle TOP will be broken up into 2 = parts, and part of the given information is the Measure of Angle TOS, which gives us the other part of TOP. Also in the given information is the fact that OM is perpendicular to OP which creates a right angle at the vertex, which gives you 90˚ to = the measure of TOP to so you can get a single number.
Answer- 54˚
9. To get this answer all you have to do is add up all of the angles of the triangle, and divide that by 180˚ because there is 180˚ in a triangle. After you do this you have to plug in the number you get to each equation, and you can classify the triangle by its angles.
Answer- Scalene
10. We are given the Measure of Angle ACB, which is part of the triangle that contains the angle we need to find. We are also given the Measure of Angle FCG which is vertical to Angle ACB; this gives us something to find out a true ˚. Lastly we are given the Measure of Angle ABD which helps us find the Measure of Angle DBC because it is an exterior angle of Triangle DBC. Subtract the Measure of Angle ABD from 80 and you get the 2nd needed angle in the Triangle DBC. Add those to Numbers together and we are left with the measure of Angle DBC.
Answer- 82.5˚
if anyoine feels like reading it HELP me out.... i need help in g30m3try
