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Math Help - Triangles.

  1. #1
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    Triangles.

    1. It is impossible for a triangle to be which of the following?
    1. both isosceles and right
    2. both equilateral and equiangular
    3. both scalene and acute
    4. both obtuse and equilateral
    2. From the markings shown on the following triangle, which of the following statements is true?
    1. is an isosceles, right triangle.
    2. is an equilateral, right triangle.
    3. is an isosceles, acute triangle.
    4. is an equiangular, acute triangle.

    3. In if and , then
    1. is a scalene triangle
    2. is an acute triangle
    3. is a right triangle
    4. is an isosceles triangle
    4. In if is one inch longer than is 10 inches shorter than the sum of and , and the perimeter of is 72 inches, find the length of .
    1. 20 in.
    2. 21 in.
    3. 31 in.
    4. 32 in.
    5. If the largest angle of an isosceles triangle measures 106, find the measure of the smallest angle.
    1. 37
    2. 42
    3. 53
    4. 74
    6. In a right triangle, if one acute angle has measure and the other has measure , find the larger of these two angles.
    1. 13
    2. 22
    3. 47
    4. 68
    Use the following figure to answer questions 7-13.

    7. If and , find .
    1. 32
    2. 84
    3. 94
    4. 96
    8. Let , and . Find .
    1. 24
    2. 58
    3. 98
    4. 132
    9. If , then
    10. If , then
    11. In order to prove that by ASA, we would need to show that
    12. If , then we can prove that by
    1. SSS
    2. SAS
    3. ASA
    4. AAS
    13. If , which of the following statements is true?
    1. by ASA.
    2. by SAS.
    3. by SSA.
    4. We cannot prove that .
    For questions 14-20 complete the proof of Theorem 4.12 by selecting the best reason or statement.
    Theorem 4.12 Medians of congruent triangles are congruent.


    14. The best statement for reason 6 of this proof is
    1. D is the midpoint of .
    15. The best reason for statement 7 of this proof is
    1. congruent angles form congruent segments
    2. definition of perpendicular segments
    3. definition of a midpoint
    4. reflexive property
    16. The best statement for reason 10 of this proof is
    1. H is the midpoint of .
    17. The best reason for statement 11 of this proof is
    1. congruent angles form congruent segments
    2. definition of perpendicular segments
    3. definition of a midpoint
    4. reflexive property
    18. The best reason for statement 14 of this proof is
    1. substitution property of equality
    2. definition of congruent segments
    3. CPCTC
    4. given
    19. The best reason for statement 16 of this proof is
    1. SSS
    2. SAS
    3. ASA
    4. AAS
    20. The best reason for statement 17 of this proof is
    1. substitution property of congruence
    2. definition of congruent segments
    3. CPCTC
    4. definition of a median
    Use the following figure to answer question 21.

    21. From the construction marks shown in the diagram, we can tell that is
    1. an altitude of
    2. an angle bisector of
    3. a median of
    4. a perpendicular bisector of
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  2. #2
    Moo
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    Hello,

    This is a lot...

    Where do you have difficulties ?
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    Quote Originally Posted by Moo View Post
    Hello,

    This is a lot...

    Where do you have difficulties ?

    3, 8, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21.
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    Quote Originally Posted by ChristieZissler View Post
    3. In if and , then
    1. is a scalene triangle
    2. is an acute triangle
    3. is a right triangle
    4. is an isosceles triangle
    The sum of the interior angles of any triangle is 180 degrees. So what is the measure of angle O?

    Does this triangle contain an obtuse angle? A right angle? Are any of the angle measures equal?

    -Dan
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ChristieZissler View Post

    8. Let , and . Find .
    1. 24
    2. 58
    3. 98
    4. 132
    Well, angle EBA, angle EBD, and angle DBC are all part of a straight angle. So angle EBA + angle EBD + angle DBC = 180 degrees. That will give you x. So now you know two angles of triangle BCD. How do you find the third angle of this?

    -Dan
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  6. #6
    Moo
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    What does m< represent ? (in 8.)
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  7. #7
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ChristieZissler View Post
    Use the following figure to answer questions 7-13.

    11. In order to prove that by ASA, we would need to show that
    Give this one another try. It's a definition. ASA means angle-side-angle. Angles EBA and DBC are equal, sides AB and CB are equal, so we would need to know what more to prove these congruent by ASA?

    -Dan
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Moo View Post
    What does m< represent ? (in 8.)
    m<A stands for the "measure of angle A."

    -Dan
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  9. #9
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    Quote Originally Posted by ChristieZissler View Post
    21. From the construction marks shown in the diagram, we can tell that is
    1. an altitude of
    2. an angle bisector of
    3. a median of
    4. a perpendicular bisector of
    This is the basic construction for an angle bisector...

    Construction: Bisect Angle
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