How do you prove that two triangles on the same base and between the same parallels are equal in area?
Table of Contents
- 1 How do you prove that two triangles on the same base and between the same parallels are equal in area?
- 2 What is the relation between area of parallelogram and rectangle standing on same base and between same parallel?
- 3 How do you measure a parallelogram?
- 4 How do you prove that two triangles have the same area?
- 5 Do parallelograms and rectangles have the same area?
- 6 How do you describe two opposite angles in a parallelogram?
How do you prove that two triangles on the same base and between the same parallels are equal in area?
The area of each triangle is half of the area of any parallelogram on the same base and between the same parallels. Thus, the area of the two triangles is the same. Let us formalize this as a theorem: Theorem: Two triangles on the same base and between the same parallels are equal in area.
What is the relation between area of parallelogram and rectangle standing on same base and between same parallel?
Parallelograms and rectangles on same base and between same parallels are equal in area.
What do you say about area of parallelogram on the same base and between the same parallels?
Theorem: A parallelogram on the same base and between the same parallels are equal in area.
How do you measure a parallelogram?
Where, b = base of the parallelogram (AB) h = height of the parallelogram. a = side of the parallelogram (AD)…Area = ½ × d1 × d2 sin (y)
| All Formulas to Calculate Area of a Parallelogram | |
|---|---|
| Using Base and Height | A = b × h |
| Using Trigonometry | A = ab sin (x) |
How do you prove that two triangles have the same area?
Areas of similar triangles are proportional to the squares on their corresponding sides. If the triangles are congruent then the areas are equal.
How the areas of a triangle and a parallelogram with the same base and height are related?
1. If a triangle and parallelogram are on the same base and have the same altitude, the area of the triangle will be half that of the parallelogram. Hence the area of the triangle will be equal to half that of the parallelogram.
Do parallelograms and rectangles have the same area?
Because the parallelogram and rectangle are composed of the same parts, they necessarily have the same area. Because base × height gives the area of the rectangle, we can use the same measurements on the parallelogram to compute its area: base × height.
How do you describe two opposite angles in a parallelogram?
The opposite angles of a parallelogram are equal. The opposite sides of a parallelogram are equal. The diagonals of a parallelogram bisect each other.