Square Diagonal Properties: Classifying Triangles ABC and ACD

AAABBBCCCDDD

ABCD is a square with AC as its diagonal.

What kind of triangles are ABC and ACD?

(There may be more than one correct answer!)

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 How can we define the triangles formed by the diagonal of a square?
00:03 In a square all angles are right angles
00:07 A triangle with a right angle is a right triangle
00:10 The diagonal in a square bisects the angle
00:14 A triangle with equal base angles is isosceles
00:19 The same thing happens in the second triangle,
00:22 This is the solution

Step-by-step written solution

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1

Understand the problem

AAABBBCCCDDD

ABCD is a square with AC as its diagonal.

What kind of triangles are ABC and ACD?

(There may be more than one correct answer!)

2

Step-by-step solution

Since ABCD is a square, all its angles measure 90 degrees.

Therefore, angles D and B are equal to 90°, that is, they are right angles,

Therefore, the two triangles ABC and ADC are right triangles.

In a square all sides are equal, therefore:

AB=BC=CD=DA AB=BC=CD=DA

But the diagonal AC is not equal to them.

Therefore, the two previous triangles are isosceles:

AD=DC AD=DC

AB=BC AB=BC

3

Final Answer

Right triangles

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In a right triangle, the side opposite the right angle is called....?

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