Take identical cut out of congruent triangle of sides 3cm,4cm,5cm. You get a trapeziums. (check it!)which are the parallel sides here? Should the non-parallel sides be equal?
Take identical cut
identical to what?
Do you mean to cut off each corner of the triangle? guess not.
what do you mean by "take a cut out of a triangle"?
Maybe you could describe things a bit. So,
Start with triangle ABC with sides a=3, b=4, c=5
then ...
To create a trapezium by taking identical cut outs from a congruent triangle with sides 3cm, 4cm, and 5cm, we need to consider the properties of a trapezium.
A trapezium is a quadrilateral with one pair of parallel sides. In this case, the congruent triangle has no parallel sides. So, when we take identical cut-outs from the triangle to form a trapezium, we need to ensure that one pair of sides becomes parallel.
To do this, we can cut one side of the triangle and move it to another side, aligning them in parallel, while keeping the other sides joined. Let's take the 3cm side and move it to the opposite side of the triangle. After doing this, the trapezium will have parallel sides of 4cm and 3cm.
Regarding the non-parallel sides, in general, they will not be equal in a trapezium. However, in this specific case, since we are forming a trapezium from a congruent triangle, the non-parallel sides will be equal. So, both non-parallel sides of the trapezium will have lengths of 5cm.
To summarize:
Parallel sides of the trapezium: 4cm and 3cm.
Non-parallel sides of the trapezium: 5cm (both sides).
To determine the parallel sides of the trapezium formed by taking an identical cutout of a congruent triangle, we need to follow these steps:
1. Start with a congruent triangle with sides measuring 3cm, 4cm, and 5cm.
2. Cut out an identical copy of this triangle, ensuring that the shape and size are exactly the same.
3. Position the two congruent triangles next to each other in a way that aligns their corresponding sides.
4. Together, the two congruent triangles will form a trapezium.
Now let's determine the parallel sides of this trapezium and whether the non-parallel sides are equal:
In a trapezium, the parallel sides are the two sides that are parallel to each other. To identify them, examine the lengths of the corresponding sides of the congruent triangles.
Let's label the congruent triangles as triangle A and triangle B, and the sides of trapezium as AB, BC, CD, and DA.
The corresponding sides of triangle A and triangle B are as follows:
- The side with length 3cm in triangle A corresponds to the side with length 3cm in triangle B. These two sides are opposite each other in the trapezium and are parallel. Therefore, AB and CD are the parallel sides.
- The side with length 5cm in triangle A corresponds to the side with length 4cm in triangle B. These two sides are adjacent to each other in the trapezium and are not parallel. Therefore, BC and DA are the non-parallel sides.
Regarding the question of whether the non-parallel sides should be equal, in general, the non-parallel sides of a trapezium are not equal. In this case, BC and DA have different lengths (5cm and 4cm), so they are not equal.
Hence, in the trapezium formed by taking an identical cutout of a congruent triangle with sides 3cm, 4cm, and 5cm, the parallel sides are AB and CD, and the non-parallel sides are BC and DA, which are not equal.