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Eighth Grade (Grade 8) Triangles Questions

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Grade 8 :: Triangles by LBeth
For the right triangle below: [math]BC^2 = AB^2 + AC^2 [/math]

Which equation is equivalent to the above equation?

Right Triangle ABC v1
  1. [math]BC = AB + AC [/math]
  2. [math]AB^2 = BC^2 - AC^2[/math]
  3. [math]AC^2 = BC^2 + AB^2 [/math]
  4. [math]AB^2 = BC^2 + AC^2 [/math]
Grade 8 :: Triangles by LBeth
Write the letter "D" at the point where the altitude meets line AC.

Given: Triangle ABC is a right triangle; [math]angB[/math] is a right angle; line BD is perpendicular to AC

Which reason explains the following:

[math](AC)/(BC) = (BC)/(DC); (AC)/(AB)=(AB)/(AD)[/math]

Acute Triangle Height v3
  1. though a point outside a line, there is exactly one line perpendicular to the given line
  2. given the altitude of a right triangle, the legs are the geometric mean of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg
  3. when the hypotenuse and a leg of a right triangle are congruent to corresponding parts of another right triangle, the triangles are congruent
  4. the sum of the side lengths of any two sides of a triangle are greater then the length of the third side
Grade 8 :: Triangles by ksilvers12
The measures of the angles in a right triangle are x, 2x and [math]90deg[/math]. What is x?
  1. [math]15deg[/math]
  2. [math]30deg[/math]
  3. [math]45deg[/math]
  4. [math]60deg[/math]
Grade 8 :: Triangles by ksilvers12
Grade 8 :: Triangles by ksilvers12
The first major ski slope in Gatlinburg had a rise of 9 feet vertically for every 54 feet horizontally. A second ski slope has a rise of 12 feet vertically for every 84 feet horizontally. Which of the following statements is true?
  1. The first slope is steeper than the second
  2. Both slopes have the same steepness
  3. The second slope is steeper than the first
  4. This cannot be determined from the information given
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