Question

In the triangles, and .

1Which statement correctly compares the angles?

Angle G is congruent to angle P.
Angle G is smaller than angle P.
Angle G is larger than angle P.
Angle G is congruent to angle N.

2Consider the triangle.
Which statement is true about the lengths of the sides?

Each side has a different length.
Two sides have the same length, which is less than the length of the third side.
The three sides have the same length.
The sum of the lengths of two sides is equal to the length of the third side.

3Lee is creating a garden with the dimensions shown.
He creates paths through the garden along , , and . Which correctly compares the lengths of the paths?

The path along is longer than the path along , and the path along is longer than the path along .
The path along is longer than the path along , and the path along is longer than the path along .
The path along is longer than the path along , and the path along is longer than the path along .
The path along is longer than the path along , and the path along is longer than the path along .

Answer 1

B. Angle G is smaller than angle P.

Explanation:

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Answer 2

The correct answers are:

#1) Angle G is smaller than angle P; #2) The three sides have the same length; #3) The path along XY is longer than the path along ZY, and the path along ZY is longer than the path along AB.

Explanation:

#1) Since the measure of HK is smaller than the measure of MN, this means the angle opposite HK will be smaller than the angle opposite MN. This means ∠G is smaller than ∠P.

#2) Since all of the angles are congruent, all of the sides will be congruent as well.

#3) The side opposite the largest angle will be longest; the side opposite the smallest angle will be shortest. This means the side opposite the 36° angle, AB, will be smallest, and the side opposite the 79° angle, XY, will be largest. ZY will have a length between these two.