The hypotenuse of a right triangle is 8.2 inches long and one of the legs is 6.4 inches long. What is the length of the other leg?

Choose the correct name(s) for this angle. Check all which apply. The diagram shows two rays originating from point R. Ray RP extends upward to the right, passing through labeled points Q and P, ending in an arrow. Ray RT extends downward to the right, passing through labeled points S and T, also ending in an arrow. Points R, Q, P, S, and T are marked with solid black dots. The rays form an angle at point R.

What is the value of y? Express your answer in simplest radical form. The right triangle has the right angle at the bottom left. The base is labeled 12, and the vertical leg on the left is labeled x. The hypotenuse, slanting from top left to bottom right, is labeled y. The angle at the bottom right is marked 30 degrees. All sides are outlined in bold black lines.

Fill in each missing reason.Given: Prove:  Two parallel appearing horizontal lines, each ending in double-headed arrows, extend left and right across the image. A diagonal line with arrowheads at both ends crosses the parallel lines from the upper right to the lower left. This intersection forms three clearly labeled angles. Angle 1 is located above the top parallel line on the left side of the diagonal. Angle 2 is above the bottom parallel line, also on the left side of the diagonal. Angle 3 lies opposite angle 2, positioned below the bottom parallel line on the right side of the diagonal. All lines are solid black. Statements Reasons a. Given b. [answer1] c. [answer2] d. [answer3]  

In order to walk to school from your house, you walk 0.8 mi north and 0.5 miles east. What is the direct distance from your house to school?

On a coordinate plane, a line segment has end points at and .  What is the midpoint? ( [answer0] , [answer1] )  

Find the value of x.  The triangle is oriented with its apex pointing upward. An exterior angle labeled 118 extends horizontally from the left vertex. The interior angle at the bottom right is labeled 54, and the interior angle at the top vertex is labeled x. All sides are drawn with bold black lines.

Which angles are alternate interior angles? “Two horizontal parallel appearing lines are intersected by two diagonal lines slanted to the left. This setup creates four intersection points, while each intersection forms four angles. The angles are numbered 1 through 16, which are labeled as follows: Top-left intersection: angles 1 (top-left), 2 (top-right), 5 (bottom-right), 6 (bottom-left) Top-right intersection: angles 3 (top-left), 4 (top-right), 7 (bottom-right), 8 (bottom-left) Bottom-left intersection: angles 9 (top-left), 10 (top-right), 13 (bottom-right), 14 (bottom-left) Bottom-right intersection: angles 11 (top-left), 12 (top-right), 15 bottom-right), 16 (bottom-left)”

The length of is shown. What other length can you determine for this diagram?  The slanted quadrilateral FGDE is outlined in black. Side GD is at the top, and side FE is at the bottom. Diagonals DF and GE intersect at a right angle, marked by a small square at the center of the left quadrant. Diagonal DF is divided into two equal segments by diagonal GE, indicated by tick marks. The side DE is labeled 12. Other sides and segments are unlabeled,

Select the image below that represents the construction of an angle bisector.