Is the following statement true? Why?
“Two quadrilaterals are similar if their corresponding angles are equal.”
False.
Step 1: Recall the meaning of "similar figures".
Two figures are called similar if:
Step 2: Check what the statement says.
The statement says that only equal angles are enough to make two quadrilaterals similar.
Step 3: See why this is not correct.
For polygons with more than 3 sides (like quadrilaterals), equal angles alone are not sufficient. We must also check the ratio of sides.
Step 4: Example to understand better.
Take two rectangles:
Both rectangles have all four angles = (90^circ). So, their angles are equal.
But the ratio of sides is different:
Since the side ratios are not the same, these two rectangles are not similar.
Final Conclusion: The statement is false. For similarity of quadrilaterals, both equal angles and proportional sides are required.