Question

which statements about triangles are true? select all that apply.
□ two triangles can be put together to form a parallelogram.
□ 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 diagonal can split a rectangle with an area of 40 square units into two triangles with areas of 20 square units each.
□ 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 congruent triangles can be put together to form a parallelogram.

Step2: Analyze the second statement

The area formula of a triangle is \(A=\frac{1}{2}bh\), not \(A = 2bh\).

Step3: Analyze the third statement

The area of a rectangle is \(A_{r}=bh\), and the area of a triangle is \(A_{t}=\frac{1}{2}bh\). So all triangles have an area that is one - half the area of a rectangle with the same base and height.

Step4: Analyze the fourth statement

If the area of a rectangle is \(A = bh=40\), then the area of each triangle formed by the diagonal is \(A_{t}=\frac{1}{2}bh\). Substituting \(bh = 40\), we get \(A_{t}=20\).

Step5: Analyze the fifth statement

The area of the triangle is \(A_{t}=\frac{1}{2}\times4\times4 = 8\), and the area of the square is \(A_{s}=4\times4=16\). So the triangle has a smaller area.

Answer:

• First statement: True
• Second statement: False
• Third statement: True
• Fourth statement: True
• Fifth statement: False

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