Question

which statements about triangles are true? choose three correct answers.
two triangles can be put together to form a parallelogram.
a diagonal can split a rectangle with an area of 40 square units into two triangles with areas of 20 square units each.
the area of a triangle can be found using the formula ( a = 2bh ).
all triangles have an area that is one half the area of a rectangle with the same base and height.
a triangle with a base and height of 4 units has a greater area than a square with the same dimensions.

Explanation:

Step1: Analyze the first statement

Two triangles can be put together to form a parallelogram. This is a well - known geometric property.

Step2: Analyze the second statement

A diagonal can split a rectangle with an area of 40 square units into two triangles with areas of 20 square units each. Since the diagonal of a rectangle divides it into two congruent triangles, each triangle has half the area of the rectangle.

Step3: Analyze the fourth statement

All triangles have an area that is one half the area of a rectangle with the same base and height. The formula for the area of a triangle is \(A=\frac{1}{2}bh\) and for a rectangle is \(A = bh\).

Step4: Analyze the third statement

The formula for the area of a triangle is \(A=\frac{1}{2}bh\), not \(A = 2bh\). So this statement is false.

Step5: Analyze the fifth statement

A triangle with a base and height of 4 units has an area \(A=\frac{1}{2}\times4\times4=8\) square units. A square with side length 4 has an area \(A = 4\times4=16\) square units. So a triangle with base and height of 4 units has a smaller area than a square with the same dimensions. This statement is false.

Answer:

• Two triangles can be put together to form a parallelogram.
• A diagonal can split a rectangle with an area of 40 square units into two triangles with areas of 20 square units each.
• All triangles have an area that is one half the area of a rectangle with the same base and height.