In a quadrilateral, if one angle is 90 degrees and the opposite angle is 90 degr
Practice Questions
Q1
In a quadrilateral, if one angle is 90 degrees and the opposite angle is 90 degrees, what can be concluded about the quadrilateral?
It is a rectangle.
It is a square.
It is a parallelogram.
It is a trapezium.
Questions & Step-by-Step Solutions
In a quadrilateral, if one angle is 90 degrees and the opposite angle is 90 degrees, what can be concluded about the quadrilateral?
Step 1: Understand what a quadrilateral is. A quadrilateral is a shape with four sides and four angles.
Step 2: Identify the angles in the quadrilateral. In this case, we have one angle that is 90 degrees and the opposite angle that is also 90 degrees.
Step 3: Recall the properties of angles in a quadrilateral. The sum of all four angles in a quadrilateral is always 360 degrees.
Step 4: Since we have two angles of 90 degrees, we can add them together: 90 + 90 = 180 degrees.
Step 5: This means that the other two angles must also add up to 180 degrees (because 360 - 180 = 180).
Step 6: If the opposite angles are both 90 degrees, the other two angles must also be right angles (90 degrees each) to maintain the properties of a rectangle.
Step 7: Therefore, if a quadrilateral has two opposite angles of 90 degrees, it must be a rectangle.
