mathan cut a rectangular tiles in half for his kitchen floor design. the tile was not a square. he made one cut along a diagonal from one vertex to another vertex. classify the two triangle resulting from the cut by their angle and their side length
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To classify the two triangles resulting from cutting the rectangular tile in half along a diagonal, we need to consider both their angle measures and side lengths.
Let's break it down step-by-step:
Step 1: Understand the problem and gather information.
- Mathan cut a rectangular tile in half along a diagonal.
- The tile is not a square.
Step 2: Visualize the situation.
- Draw a rectangle representing the original tile.
- Draw a line connecting one vertex (corner) of the rectangle to another vertex, creating a diagonal that cuts the rectangle in half.
Step 3: Analyze the angles of the triangles.
- Triangles are classified based on their angles.
- There are six main classifications: acute, right, obtuse, equilateral, isosceles, and scalene.
Step 4: Analyze the side lengths of the triangles.
- Triangles can be further classified based on their side lengths.
- There are three main classifications: equilateral, isosceles, and scalene.
Step 5: Determine the classifications of the resulting triangles.
- Since Mathan cut the rectangle along a diagonal, the resulting triangles are right triangles. A right triangle has one 90-degree angle.
- Regarding side lengths, if the original rectangle was not a square, the two resulting triangles will be neither equilateral nor isosceles.
- Therefore, the resulting triangles are classified as right scalene triangles.
- A right scalene triangle is a triangle with one 90-degree angle and no equal sides.
Alternatively, you can verify this classification by measuring the angles and side lengths of the triangles using a ruler or protractor.