The diagonals of a square bisect each other at _________ angle.a)acute...
The diagonals of a square bisect each other at a right angle.
Explanation:
- A square is a quadrilateral with all four sides equal in length and all four angles equal to 90 degrees.
- The diagonals of a square are the line segments that connect opposite corners of the square.
- When the diagonals of a square intersect, they divide each other into two equal halves.
- Since a square has four equal angles of 90 degrees, the diagonals of a square will also intersect at a right angle.
Proof:
- Let's consider a square ABCD with diagonals AC and BD.
- The diagonal AC divides the square into two right-angled triangles, namely triangle ABC and triangle CDA.
- Similarly, the diagonal BD divides the square into two right-angled triangles, namely triangle ABD and triangle BCD.
- In each of these triangles, the two legs are equal in length because the sides of the square are equal.
- By the property of a right-angled triangle, in a triangle where the two legs are equal, the angles opposite to the legs are also equal.
- Therefore, in triangle ABC and triangle CDA, angle BAC = angle CAD = 90 degrees/2 = 45 degrees.
- Similarly, in triangle ABD and triangle BCD, angle ABD = angle CBD = 90 degrees/2 = 45 degrees.
- Since angle BAC = angle CAD and angle ABD = angle CBD, the opposite angles of the intersecting diagonals AC and BD are equal.
- By the definition of a right angle, when two lines intersect and their opposite angles are equal, the lines are perpendicular to each other.
- Hence, the diagonals AC and BD of a square bisect each other at a right angle.
Therefore, the correct answer is option 'B' - right.
The diagonals of a square bisect each other at _________ angle.a)acute...
The diagonals of a square are equal and bisect each other at right angles.
because square are equal and bisect each other side is a right angle
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