Geometry

4 Rectangle ABCD with diagonals intersecting at O. OA = 22 yd, OD = ___ angle BAD = ___, angle ABC = ___

Step-by-step solution with explanation

Final Answer

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Step-by-step solution

1

Recall key rectangle diagonal properties

In any rectangle, the two diagonals are equal in length and they cut each other exactly in half at their intersection point O. This means all four segments from O to a corner are equal.
2

Find OD using diagonal bisection

Since the diagonals bisect each other, O is the midpoint of both diagonals. So OD equals OA, which is 22 yd.
3

Identify angle BAD in a rectangle

A rectangle has four right angles by definition. So every interior angle, including angle BAD, measures exactly 90°.
4

Identify angle ABC in a rectangle

Again, all interior angles of a rectangle are right angles. Angle ABC is also 90°.

Understanding this problem

Learning Insight

The diagonals of a rectangle are congruent (same length) and bisect each other. This means the four triangles formed inside the rectangle are all congruent isosceles triangles. The equal segments from O to each corner come directly from this bisection property.

Quick Tip

For ANY rectangle problem: all angles = 90°, and the diagonals are equal AND bisect each other. So if you know one half-diagonal, you know all four.

Common Mistake

Students often confuse 'bisect' with 'perpendicular bisect.' Rectangle diagonals DO bisect each other (equal halves), but they are NOT perpendicular to each other (that's a square or rhombus). Don't assume OA is perpendicular to OB.