Square Diagonal Analysis: Identifying Triangle Types in a Square ABCD

Triangle Classification with Diagonal Intersections

Look at the square below:

AAABBBDDDCCC

What types of triangles do the diagonals in the square form?

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the square below:

AAABBBDDDCCC

What types of triangles do the diagonals in the square form?

2

Step-by-step solution

The diagonals of the square intersect each other, so the four triangles are isosceles. Moreover, since the diagonals are perpendicular to each other, the diagonals form four right-angled triangles. Therefore, the correct answers are A+C

3

Final Answer

Answers (a) and (c) are correct.

Key Points to Remember

Essential concepts to master this topic
  • Properties: Square diagonals are perpendicular and bisect each other
  • Analysis: Four triangles have two equal sides and 90° angles
  • Check: All triangles are both right-angled AND isosceles ✓

Common Mistakes

Avoid these frequent errors
  • Choosing only one triangle type instead of both
    Don't pick just right-angled OR just isosceles = missing half the answer! Each triangle has BOTH properties simultaneously. Always identify ALL triangle classifications that apply to the same triangles.

Practice Quiz

Test your knowledge with interactive questions

Look at the square below:

Is a parallelogram a square?

FAQ

Everything you need to know about this question

How can a triangle be both right-angled AND isosceles at the same time?

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A triangle can have multiple classifications! When square diagonals intersect, they create triangles with two equal sides (isosceles) and one 90° angle (right-angled). These properties don't conflict - they describe different features of the same triangle.

Why are the diagonals of a square perpendicular?

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In a square, diagonals always meet at 90° angles because of the square's symmetry. This perpendicular intersection is what creates the right angles in each of the four triangles formed.

How do I know the triangles are isosceles?

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Each triangle has two sides that are equal - they're both half the length of a diagonal. Since the diagonals bisect each other, the two segments from the center to any two vertices of the square are equal lengths.

Are all four triangles exactly the same?

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Yes! All four triangles are congruent - they have the same size and shape. Each one is both right-angled and isosceles with the same measurements.

What if I only see right angles and miss the equal sides?

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Look carefully at the diagonal segments! From where the diagonals cross to each vertex of the square, you'll see that two sides of each triangle are equal - that's what makes them isosceles.

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