Determine whether or not the triangle each pair below are congruent. Justify your conclusion.

  a, b, d — congruent

  c — not congruent

Step-by-step explanation:

a) Both right triangles have side lengths of 6, 8, and 10. (In each triangle, two of those numbers are given. The third is found using the Pythagorean theorem, or by simply matching these numbers to the Pythagorean triple (6, 8, 10). Given any two sides of a right triangle, there is no doubt as to the measure of the third one.

The triangles are congruent by SSS. (For SSS, you do have to find the measure of the missing side.)

__

b) The triangles are congruent by AAS. Corresponding sides and angles are marked congruent.

__

c) The triangles are not congruent. Two sides are congruent, but the marked angles are not corresponding. One triangle has no necessary relationship to the other.

__

d) The triangles are congruent by SAS. The marked angle is between a shared side and the marked side. The shared side of the triangles is actually a diagonal of the parallelogram (figure is not to scale).

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.