Which postulate or theorem, if any, could you use to show the two triangles are congruent? Choose all that apply. Two upward-pointing triangles meet at a shared vertex along a horizontal base. The right vertex of the left triangle and the left vertex of the right triangle coincide at this common point. In each triangle, two interior angles are marked as congruent—one at the apex and one at the outer base corner. Tick marks on the sides connecting each apex to the shared base vertex indicate that these corresponding sides are congruent. The triangles are arranged symmetrically on either side of the shared vertex. All edges are bold black lines, and angle arcs highlight the marked interior angles.

Triangles MNL and ZXY are congruent. Which angle corresponds to angle L?  The image shows two blue-outlined triangles: MNL on the left and ZXY on the right. The triangles are congruent but oriented differently. The horizontal side LN in triangle MNL corresponds to side XY in triangle ZXY. Similarly, the longer slanted side MN corresponds to side XZ, and the shorter slanted side LM corresponds to side YZ.

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)”