Find the circumcenter of the triangle. A triangle is plotted on a coordinate grid. The x-axis spans from negative six to five, and the y-axis spans from negative four to six, both marked at intervals of one. The triangle’s vertices are at (negative 3, 3), (negative 3, negative 2), and (1, negative 2). The left side is a vertical segment from (negative 3, 3) to (negative 3, negative 2). The bottom side is a horizontal segment from (negative 3, negative 2) to (1, negative 2). The diagonal side, forming the hypotenuse, connects (1, negative 2) to (negative 3, 3).

Under the UNESCO Convention on the Protection of Underwater Cultural Heritage, underwater traces of human existence that are 100 years old or more are protected.

Find the length of one of the legs. The right triangle is oriented with a horizontal base at the top, a vertical leg on the right, and a hypotenuse slanting downward from the top left to the bottom right. A right angle is marked with a small square at the top right corner, and the top left angle is labeled 45 degrees. The hypotenuse is labeled as six times the square root of two. All sides are outlined in bold black lines.

AC and BD are perpendicular bisectors of each other. Find the measurement of AB. Quadrilateral ABCD has vertical diagonal AC and horizontal diagonal DB intersecting at point E. Vertex A is at the top, C at the bottom, D on the left, and B on the right. Point E lies on both diagonals, dividing them into segments AE and EC vertically, and DE and EB horizontally. Segment DE is labeled 12, and segment EC is labeled 5. Other sides and segments are unlabeled,

Complete the missing reason in the two column proof: Given: Line LN is perpendicular to line AB Prove: is supplementary to Perpendicular lines AB and LN intersect at point M. Points A, B, L, and N are marked with solid dots at each end, and M is marked at the center. The lines are blue with arrowheads on ends L and N. Statements Reasons  1. Line LN is perpendicular to line AB  1. Given  2. and measure 90 degrees  2. Definition of Perpendicular  3. = 180 degrees  3.Angle Addition Postulate  4. is supplementary to  4. ?

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.