Square Diagonal Intersection: Analysis of a 5 cm Square

If side AC of the square measures 5 cm:

Determine whether the diagonals of the square intersect:

555AAABBBDDDCCC

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Do the diagonals intersect in a square?
00:10 In a square, all sides are the same length, and each angle is a right angle.
00:16 The diagonals in a square are angle bisectors, splitting the angles into two equal parts.
00:22 If a triangle has two equal base angles, it's called isosceles. Remember this!
00:30 This is true for every triangle formed by the diagonals.
00:36 Since all these triangles are isosceles, the diagonals definitely intersect.
00:42 And that's how we solve this problem!

Step-by-step written solution

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1

Understand the problem

If side AC of the square measures 5 cm:

Determine whether the diagonals of the square intersect:

555AAABBBDDDCCC

2

Step-by-step solution

In a square all sides are equal to one another, meaning that all the sides measure 5 cm.

Furthermore in a square, all angles are equal, they are right angles and measure 90 degrees.

Therefore, we can determine that the diagonal divides each angle into 2 angles of 45 degrees, thus the diagonals must intersect.

3

Final Answer

Yes

Practice Quiz

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Look at the square below:

Is a parallelogram a square?

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