Yes, both triangles are constructible. A triangle is constructible if its three sides can be constructed using a straightedge and compass. In the case of the first triangle, we can construct the sides of length 3, 4, and 5 using the Pythagorean theorem. For the second triangle, we can construct the sides of length 5, 7, and 8 using the Pythagorean theorem as well. Therefore, both triangles are constructible. **

Rice triangles, also known as onigiri, are a popular Japanese snack made of rice formed into a triangular or cylindrical shape and often wrapped in seaweed. They are typically filled with ingredients such as pickled plum, salmon, or tuna. Rice triangles are a convenient and portable snack commonly found in Japanese convenience stores and are enjoyed for their delicious flavor and satisfying texture. **

Similar triangles are triangles that have the same shape but are not necessarily the same size. This means that their corresponding angles are equal and their corresponding sides are in proportion to each other. When two triangles are similar, their sides are in the same ratio, known as the scale factor. This property allows us to use the concept of similarity to solve various geometric problems involving triangles. **

Slope triangles are a visual representation of the slope of a line on a graph. They are formed by drawing a right-angled triangle on the graph, with one side parallel to the x-axis and the other parallel to the y-axis. The slope of the line is then calculated by comparing the vertical and horizontal lengths of the triangle. Slope triangles are a helpful tool for understanding and visualizing the concept of slope in mathematics. **

Isosceles triangles are a type of triangle that has two sides of equal length. This means that two of the three angles in the triangle are also equal in measure. The third side, called the base, is typically of a different length than the other two sides. Isosceles triangles have a line of symmetry that divides the triangle into two equal halves. **

The triangles are congruent because they have the same size and shape. This means that their corresponding sides and angles are equal. In this case, the given information about the sides and angles of the two triangles allows us to conclude that they are congruent using the Side-Angle-Side (SAS) congruence criterion. Therefore, the triangles are congruent. **

Right-angled triangles are a type of triangle that has one angle measuring 90 degrees, which is known as the right angle. The side opposite the right angle is called the hypotenuse, and it is the longest side in the triangle. The other two sides are called the legs of the triangle. Right-angled triangles have a special property known as the Pythagorean theorem, which relates the lengths of the sides of the triangle. This theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. **

Without seeing the triangles in question, it is difficult to determine if they are correctly labeled. However, if the triangles are labeled based on their angles and side lengths, it is important to ensure that the labels accurately reflect the properties of each triangle. For example, a triangle labeled as "equilateral" should have all three sides of equal length, while a triangle labeled as "right-angled" should have one angle measuring 90 degrees. It is important to carefully examine the properties of each triangle to determine if they are correctly labeled. **